Question

The height of a triangular window is 3 feet less than its base. The area the window is 20 ft.? find the dimensions of the window

Answer 1

Let us assume base of the window = b feet.

Height is 3 feet less than base, that is = (b-3).

Given area of the triangle = 20 feet square.

We know formula for area of a triangle:

Area = $\frac{1}{2}$ × Base × Height

Plugging values in formula, we get

20 = $\frac{1}{2} b \times (b-3)$

$\mathrm{Multiply\:both\:sides\:by\:}2$

$40=b\left(b-3\right)$

$40=b^2-3b$

$b^2-3b-40=0$

Factoring quadratic, we get

$\left(b+5\right)\left(b-8\right)$=0

b+5=0

b=-5

b-8=0

b=8.

For base we can take only positive value.

Therefore, base of the triangle = 8 feet and height = 8 -3 = 5 feet.