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The base of a triangle exceeds its height by 17 inches. If its area is 55 square inches, find the base
and height of the triangle.
 one year ago
 one year ago
The base of a triangle exceeds its height by 17 inches. If its area is 55 square inches, find the base and height of the triangle.
 one year ago
 one year ago

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MBrecht92Best ResponseYou've already chosen the best response.0
I thought I should set up the problem this way: 55 = 1/2(h+h+17)
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
But then I got the wrong answer, as usual
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
let h = height, then let b = base = h + 17 Area of triangle: A = (bh)/2 55 = (h + 17)h/2
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
Right, exactly..so 55 = 2h+17/2, and thus h+17/2 = 55. Then, 55*2 = h+17
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Your're close, but the formula for the area of a triangle is the base times the height over 2, not the base plus the height over 2.
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
right \[ \large 55=\frac{(h+17)\cdot h}{2} \]
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
Um...but I already multiplied the b by the h. It's just that here, b = h + 17
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
it's not (2h + 17)/2 = 55, it's (h^2 + 17h)/2 = 55
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
use the distributive law on the denominator
 one year ago

helder_edwinBest ResponseYou've already chosen the best response.0
\[ \large 55=\frac{h^2+17h}{2} \]
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
Okay. So you end up with h^2 + 17h = 110
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Right. Now subtract the 110 to the left and solve the quadratic eq.
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Set it equal to zero and solve.
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
(x+22)(x5) = 0, x = 22, 5
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
Sorry...I meant h. So h = 5, and then b = (5) + 17 = 22
 one year ago

MBrecht92Best ResponseYou've already chosen the best response.0
Thank you for all your help!!
 one year ago

mathstudent55Best ResponseYou've already chosen the best response.1
Not x, but h. Now you have h = 22 or h = 5. A negative number is meaningless as the height of a triangle, so dicard it. yes, you got it.
 one year ago
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