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ICE Princess25 [194]
3 years ago
7

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 th

e measures of the base and height.
Mathematics
1 answer:
Pani-rosa [81]3 years ago
6 0

Answer:

  base = 8 in; height = 3 in

Step-by-step 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.

_____

<em>Comment on the solution</em>

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.

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