SOLUTION: the area of a right-angled tiangles is 20 cm@. The height and the base of the triangle are (l+2) and (l-4) respectively, where l is a positive integer in cm. Find the possible valu

Algebra ->  Testmodule -> SOLUTION: the area of a right-angled tiangles is 20 cm@. The height and the base of the triangle are (l+2) and (l-4) respectively, where l is a positive integer in cm. Find the possible valu      Log On


   

Question 157273: the area of a right-angled tiangles is 20 cm@. The height and the base of the triangle are (l+2) and (l-4) respectively, where l is a positive integer in cm. Find the possible value of l.
Answer by orca(409) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the area of a triangle is:
A+=+%281%2F2%29bh
where A is the area, b is the base and h is the corresponding height.
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As its area is 20, we have
%281%2F2%29%28L-4%29%28L%2B2%29=20
Solving the equation for L, we obtain
%28L-4%29%28L%2B2%29=40
L%5E2-2L-8=40
L%5E2-2L-48=0
%28L-8%29%28L%2B6%29=0
So
L = 8, or L = -6 (reject this root, as the length can not be negative)
Thus the two lengths are:
The length of the height is L+2 = 8+2 = 10cm.
The length of the base is L-4 = 8-4 = 4cm.