Question

The area of a triangle is 12 in.^2 . The base of the triangle measures 2 in. more than twice the height of the triangle. Find the measures of the base and height.

Answer 1

base = 8 in; height = 3 in

Explanation:

Let h stand for the height of the triangle. Then 2h+2 will be the base length, and the area is ...

A = 1/2bh

12 = 1/2(2h+2)(h) = (h+1)(h)

We know that factors of 12 that differ by 1 are 4 and 3, so we conclude ...

h = 3

2h+2 = 8

Both dimensions are in inches.

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Comment on the solution

If you work through the solution of the quadratic, you find solutions are ...

h = -4, h = 3

That is, the pairs (-4, -3) and (3, 4) are both pairs of (h, h+1) that have a product of 12.

The negative solution is extraneous.