SOLUTION: The area of a right triangle is 30 square inches. The ratio of its legs is 1: 30. Find the number of inches in the hypotenuse of the triangle.

Algebra ->  Triangles -> SOLUTION: The area of a right triangle is 30 square inches. The ratio of its legs is 1: 30. Find the number of inches in the hypotenuse of the triangle.       Log On


   

Question 885943: The area of a right triangle is 30 square inches. The ratio of its legs is 1: 30. Find the number of inches in the hypotenuse of the triangle.
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
That ratio lets you say if x is the short leg then the long leg is 30x.
Pythagorean Theorem gives x%5E2%2B%2830x%29%5E2=h%5E2, but you do not yet know h, the hypotenuse.
The area is 30=%281%2F2%29x%2A30x, which is %281%2F2%29%28base%29%28height%29.

30=%281%2F2%2930x%5E2
Divide by 30
%281%2F2%29x%5E2=1
x%5E2=2
x=sqrt%282%29
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h%5E2=%28sqrt%282%29%29%5E2%2B30%5E2%2A%28sqrt%282%29%29%5E2
h%5E2=2%2B900%2A2
h%5E2=1802
highlight%28h=sqrt%281802%29%29, and 1802=2*17*53, unrepeated prime numbers.