SOLUTION: The base of a triangle is 2 in. longer than the height. The area is 12 in. to the second power . Find the height and the base. Could some one help please! Thank you!

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Question 373985: The base of a triangle is 2 in.
longer than the height. The area is 12 in. to the second power . Find the
height and the base.
Could some one help please! Thank you!
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Given the base = height + 2 or:
b+=+h%2B2
And the area is 12 sq.in.
Start with the formula for the area of a triangle:
A+=+%281%2F2%29b%2Ah Substitute A+=+12 and b+=+h%2B2
12+=+%281%2F2%29%28h%2B2%29%2Ah Simplify by multiplying by 2.
2%2812%29+=+2%281%2F2%29%28h%2B2%29%2Ah Simplify.
24+=+%28h%2B2%29%2Ah or
24+=+h%5E2%2B2h Rearrange into standard quadratic equation form.
h%5E2%2B2h-24+=+0 Solve by factoring.
%28h-4%29%28h%2B6%29+=+0 Apply the zero product rule.
h-4+=+0 or h%2B6+=+0 which means that...
h+=+4 or h+=+-6 Discard the negative solution as height (h) is a positive quantity.
h+=+4
The height is 4 inches and the base is 6 (h+2)inches.