SOLUTION: Triangle RAT is an isoceles right triangle with right angle T and area 50 cm. squared. find the lengths of the legs and hypotenuse.

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Question 198854: Triangle RAT is an isoceles right triangle with right angle T and area 50 cm. squared. find the lengths of the legs and hypotenuse.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the formula for the area of a triangle:
A+=+%281%2F2%29b%2Ah In an isosceles triangle, as in this problem, the b and h are equal, let's call them x, and the area is given as 50sq.cm., so...
50+=+%281%2F2%29%28x%2Ax%29 Multiply both sides by 2.
100+=+x%5E2 Take the square root of both sides.
x+=+10
Each of the legs is 10 cm.
The hypotenuse (c) can be found by the Pythagorean theorem:c%5E2+=+a%5E2%2Bb%5E2, where a = 10cm. and b = 10cm.
c%5E2+=+10%5E2%2B10%5E2
c%5E2+=+100%2B100
c%5E2+=+200 Take the square root of both sides.
c+=+sqrt%28200%29
c+=+14.14cm. Approx.