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

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) (Show Source): You can put this solution on YOUR website!
The formula for the area of a triangle is:

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

Solving the equation for L, we obtain

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.

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