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anonymous
 one year ago
Find the area & perimeter of the figure
anonymous
 one year ago
Find the area & perimeter of the figure

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You were given a triangle like this: dw:1437006808180:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1What do the circled marks mean? dw:1437006848302:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@11.seventeen what do the circled marks mean

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0doesn't it mean its equal

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Yes. All sides are congruent. That means every side of this triangle measures 2a mm. That makes the perimeter easy to find. What is the perimeter of a triangle?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large P_{triangle} = a + b + c\) where a, b, and c are the lengths of the sides of the triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(P = 2a + 2a + 2a = 6a\) The perimeter of the triangle is 6a mm

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes. It's the same as what i got @mathstudent55

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now you have to find the area.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0And I would do that how ? Because I don't have the heigh . I have the base is 2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1To find the area, you need to find the height of the triangle since the formula for the area involves the height.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Have you heard about the ratios of the lengths of the sides of a 306090 triangle?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes but I never understood it

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. I'll explain it to you. Here is a triangle with a right angle and a 30deg angle and a 60deg angle. dw:1437011007751:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Since the right angle is 90 deg, this triangles' three angles have measures 30, 60, and 90 degrees. This is what is called a 306090 triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1In a 306090 triangle, the length of the hypotenuse is twice the length of the short leg. If you call the length of the short leg 1, then the hypotenuse has length 2. dw:1437011223749:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The length of the long leg is \(\sqrt 3\) times the length of the short leg.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437011291789:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1So far all we have is that the lengths of the sides of a 306090 triangle are in the ratio of 1 : \(\sqrt 3 : 2\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Do you understand so far?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1It is simpler than you think. Think of \(\sqrt 3\) as being approximately 1.7 All this means is that: In a 306090 triangle, the long leg is 1.7 times the length of the short leg. The hypotenuse is 2 times the length of the short leg.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1If a 306090 triangle has a short leg of 1, then the long leg is 1.7 * 1 = 1.7 the hypotenuse is 2 * 1 = 2

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how do I get the height out of this?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Another example: If a 306090 triangle has a short leg of length 4, then the long leg is 1.7 * 4 = 6.8 and the hypotenuse is 2 * 4 = 8

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Ok. Let's get back to our problem.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437011694076:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1You see our triangle above. Since all sides are congruent, all angles are also congruent. That means all angles measure 60 degrees. Ok?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437011786387:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1We are looking for the length of the height. By drawing the height, we created two new triangles. Notice each small triangle is a 306090 triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437011853170:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Look at the figure above. Each of the two small triangles is a 306090 triangle. The 30 degree angle is above. Since the side of the large triangle has length 2a, half of that is just a, and that is the length of the short side of the 306090 triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Look at the small triangle in the circle and ignore the rest. dw:1437012005959:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The short leg has length a. The long leg has length \(\sqrt 3\) times a, which is simply: \(\sqrt 3 a\) dw:1437012059638:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437012157126:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The long leg of the small triangle is the height of the large triangle. That was the height we needed for the area.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1dw:1437012211126:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so is the height 3a?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1Now we have all the info we need to find the area of the large triangle.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1The height is \(\sqrt 3 a\), not 3a. \(\Large A_{triangle} = \dfrac{bh}{2} \)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.1\(\Large A = \dfrac{(a)(\sqrt 3 a)}{2} = \dfrac{\sqrt 3}{2}a^2 ~mm^2\)
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