SOLUTION: The side of a large tent is in the shape of an isosceles triangle whose area is 54ft^2 and whose base is 6ft shorter than twice its height. Find the height and the base of the side

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The side of a large tent is in the shape of an isosceles triangle whose area is 54ft^2 and whose base is 6ft shorter than twice its height. Find the height and the base of the side      Log On


   

Question 165441This question is from textbook
: The side of a large tent is in the shape of an isosceles triangle whose area is 54ft^2 and whose base is 6ft shorter than twice its height. Find the height and the base of the side of the tent. This question is from textbook

Answer by alicealc(293) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
triangle's base = b
triangle's height = h
b = 2h - 6

triangle's area = 54
<=>%281%2F2%29%2Ab%2Ah+=+54
<=>%281%2F2%29%2A%282h+-+6%29%2Ah+=+54
<=>%281%2F2%29%2A%282h%5E2+-+6h%29+=+54
<=>h%5E2+-+3h+=+54
<=>h%5E2+-+3h+-+54+=+0
use factorization, we will get:
(h - 9)*(h + 6) = 0
h - 9 = 0
h = 9
or
h + 6 = 0
h = -6 -> this is not a possible measure for h, because it's negative

so the value of triangle's height = 9 ft
and triangle's base = 2*9 - 6 = 18 - 6 = 12 ft