SOLUTION: One leg of a right triangle is 7cm shorter than the other leg. It's area is 30cm^2. Find its perimeter.

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Question 636302: One leg of a right triangle is 7cm shorter than the other leg. It's area is 30cm^2. Find its perimeter.
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

Note: A%5BT%5D+=+%281%2F2%29b%2Ah

One leghighlight%28y%29 of a right triangle is 7cm shorter than the other leghighlight%28x%29.

Question states*** area is 30cm^2

  30cm%5E2+=+%281%2F2%29x%2Ay      || +y+=+%28x-7%29

      60 = x(x - 7)

    x^2 - 7x - 60 = 0

   (x - 12)(x + 5) = 0   || Tossing out negative solution for unit measure

      x = 12cm   and y = 5cm

Applying the Pythagorean Theorem: sqrt%2812%5E2+%2B+5%5E2%29+=+13cm

P = 12cm + 5cm + 13cm = 30cm