SOLUTION: The area of a triangular lot is 49 square yards. The base of the lot is 7 yards less then its height. Find the length of the base and height.

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Question 823006: The area of a triangular lot is 49 square yards. The base of the lot is 7 yards less then its height. Find the length of the base and height.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Area of a triangle:
A+=+%281%2F2%29bh
Let h = height of the triangle. Then from "The base of the lot is 7 yards less then its height.":
h - 7 = base of the triangle.

Inserting the given area and these expressions into the equation for area we get:
49+=+%281%2F2%29%28h-7%29%28h%29
Now we solve for h. First we simplify:
49+=+%281%2F2%29%28h%5E2-7h%29
Multiplying by 2 (to eliminate the fraction):
98+=+h%5E2-7h
This is a quadratic equation. So we want one side to be zero. Subtracting 98 from each side:
0+=+h%5E2-7h-98
Factor:
0+=+%28h-14%29%28h%2B7%29
From the Zero Product Property:
h-14 = 0 or h+7 = 0
Solving these:
h = 14 or h = -7
We throw out the negative result since height's should not be negative. So the height of the triangle is 14 and the base, h-7, is 7.