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What is the perimeter of a right angle triangle whose height is 2.5 cm greater than its base with an area of 37.5 sq cm show work?
Wiki User
∙ 12y ago
Suppose base is B cm
Then Height is B + 2.5 cm
Area = 0.5*Base*Height = 0.5*B*(B + 2.5) which is given to be 37.5
So 0.5*B2 + 1.25*B = 37.5
That is 2B2 + 5B - 150 = 0
ie (B + 10)(2B - 15) = 0
that is B = -10 or B = 7.5
Since B is a length, it cannot be negative. So B = 7.5 cm
Then H = B + 2.5 = 10 cm
These sides are in the ratio of 3:4 (with common factor 2.5) so they form part of the Pythagorean triplet of 3:4:5. Hence the third side is 5*2.5 = 12.5 cm.
[Alternatively you can calculate the length of the hypotenuse as the square root of the sum of squares on the two sides].
And so perimeter = 7.5 + 10 + 12.5 = 30 cm
Wiki User
∙ 12y ago
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