SOLUTION: Two similiar right triangles have areas of 6 square inches and 150 square inches. The length of the hypotenuse is 5 inches. What is the sum of the legs of the larger triangle?

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Question 514051: Two similiar right triangles have areas of 6 square inches and 150 square inches. The length of the hypotenuse is 5 inches. What is the sum of the legs of the larger triangle?
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

The 5 inch hypotenuse has to be on the smaller triangle, so we know two things assuming we use and to represent the legs of the smaller triangle:

(Thank you, Mr. Pythagoras)

and

from which we can derive:

Substitute into the Pythagorean relationship

A little Algebra music, Sammy:

Let and solve the resulting quadratic for

or

Toss the negative root (we want positive real number measures of length).

Toss the negative root again

If the hypotenuse is 5 and the long leg is 4, then the short leg has to be 3 (3-4-5 right triangle).

150 divided by 5 is 30. 30 times 4 is 120, 30 times 3 is 90, 120 plus 90 is 210 which is the desired sum.

John

My calculator said it, I believe it, that settles it