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The height of a triangular window is 3 feet less than its base. Find the dimensions of the window if its area is 20 square feet.

Sagot :

Answer:

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}21 × Base × Height

Plugging values in formula, we get

20 = \frac{1}{2} b \times (b-3)21b×(b−3)

\mathrm{Multiply\:both\:sides\:by\:}2Multiplybothsidesby2

40=b\left(b-3\right)40=b(b−3)

40=b^2-3b40=b2−3b

b^2-3b-40=0b2−3b−40=0

Factoring quadratic, we get

\left(b+5\right)\left(b-8\right)(b+5)(b−8) =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.