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
^2\ +\ b^2\ =\ 25)
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
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