SOLUTION: Please help me with this question? The legs of one right triangle have a ratio of 5:12. If the hypotenuse is 65 feet in length, what is the length of the shorter leg? i know

Algebra ->  Triangles -> SOLUTION: Please help me with this question? The legs of one right triangle have a ratio of 5:12. If the hypotenuse is 65 feet in length, what is the length of the shorter leg? i know       Log On


   

Question 726330: Please help me with this question?
The legs of one right triangle have a ratio of 5:12. If the hypotenuse is 65 feet in length, what is the length of the shorter leg?
i know that i have to use pythagorean theorem, but i am not sure how.
Found 2 solutions by MathLover1, KMST:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the legs of one right triangle a and b have a ratio of 5%3A12:
a%3Ab=5%3A12
solve for a
12a=5b
a=%285b%2F12%29

if the hypotenuse c=65ft in length, use Pythagorean theorem to find the length of the shorter leg:
c%5E2=a%5E2%2Bb%5E2...substitute values a and c
%2865ft%29%5E2=%285b%2F12%29%5E2%2Bb%5E2...solve for b
4225ft%5E2=25b%5E2%2F144%2Bb%5E2...both sides multiply by 144
4225ft%5E2%2A144=25b%5E2%2B144b%5E2
608400ft%5E2=169b%5E2
608400ft%5E2%2F169=b%5E2
3600=b%5E2
b=sqrt%283600%29
highlight%28b=60%29
now find leg a
a=%285b%2F12%29
a=%285%2A60%2F12%29
a=300%2F12
highlight%28a=25%29...the length of the shorter leg
check a ratio:
a%3Ab=5%3A12
25%3A60=5%3A12
0.41666666666666666666666666666667=0.41666666666666666666666666666667...it's true, and it verifies our answer


Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Any triangle whose legs' lengths ratio is 5:12 is similar to a triangle with legs measuring 5 feet and 12 feet.
The length (in feet) of the hypotenuse of that triangle can be calculated using the Pythagorean theorem as
sqrt%285%5E2%2B12%5E2%29=sqrt%2825%2B144%29=sqrt%28169%29=13
A triangle with a hypotenuse measuring 65 feet is a 5-fold scale-up of the triangle with sides measuring 5, 12, and 13 feet.
Its sides measure
5%2A5feet=highlight%2825feet%29 ,
5%2A12feet=highlight%2860feet%29 ,
and 5%2A13feet=65feet .