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anonymous
 5 years ago
length of a rectangle is 20 meter and its are is 320 squaremeters .find the area of the square drawn on the diagonal of a square whose perimeter equals that of the given rectangle.
anonymous
 5 years ago
length of a rectangle is 20 meter and its are is 320 squaremeters .find the area of the square drawn on the diagonal of a square whose perimeter equals that of the given rectangle.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You need to find z in this set up given the info. you have.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can find z by finding x, and you find x using the information you have about the rectangle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The perimeter of the big square is equal to the perimeter of the rectangle.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If the rectangle has area 320m^2 and one side 20m, then the other side of the rectangle must be found from the formula for the area:\[A=lw \rightarrow 320=20w \rightarrow w = 16\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So the perimeter of the rectangle is 16x2 + 20x2 = 72. But we're told this is the perimeter of the big square, so the xvalue in the diagram is \[x=\frac{72}{4}=18\]since each side of a square is equal.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Now we have to use information about the side length (x) and the angles that have been made by inserting that smaller square alongside the diagonal.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The diagonal of the square bisects the angle it cuts through, so we have the following (see angles):

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I've called one side of one triangle h and the other k, so that x=h+k.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0In the bottom left triangle, we have\[\sin(45^o)=\frac{z}{h}\]but\[\sin(45^o)=\frac{1}{\sqrt{2}}\]so\[\frac{z}{h}=\frac{1}{\sqrt{2}}\]Also, in the bottom right, you have\[\sin(45^o)=\frac{z}{k}\rightarrow \frac{1}{\sqrt{2}}=\frac{z}{k}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since sin(45)=z/h=z/k, we must have h=k, and so h+k=2h=18, which means h=9.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So from any one of those two sine equations, you have\[\frac{z}{h}=\frac{1}{\sqrt{2}}\rightarrow z=\frac{h}{\sqrt{2}}=\frac{9}{\sqrt{2}}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The area of the square is\[z^2=\frac{81}{2}\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0but lokisan i dont know trignometry...i am in standard 9..

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Hmmmm...let me see if there's another way.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you taught Pythagoras' Theorem? I don't know how the Indian system works.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What are you currently learning? That might help me understand what your teacher's thinking.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Are you 'allowed' to know that the diagonals of a square bisect the right angles?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh yes.. i understood

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know you understood...I'm just trying to stick to what you're allowed to know.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0understanding has no restrictions ;) ,

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0yeah...have you covered congruence tests for triangles?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay, I'll try and put something together with that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I might have something, but I want to double check.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0hey i think i'hv got the answer ..it's coming to 648..is it correct.. ??

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You have to scrap what I wrote before too  I stuffed one of the sines up. And your 648 is a number I'm getting too.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You can do it using congruent triangles. Only catch is that you need to know that the diagonal of a square bisects the rightangle in to 45 degrees.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0okay.. thanks a lot .need to go and practice some more problems.will bug u if in need.thanx again

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Oh...okay...anyway, I got \[z= \frac{\sqrt{648}}{3}\]so that the area is \[z^2=\frac{648}{9}=72\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Congruent triangles and Pythagoras' Theorem were used.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Cool...well, if you're happy, I'm happy :)
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