SOLUTION: If two sides of right triangle are 5x and 3x-1. And area of triangle is 60 cm2 then find the hypotenuse of the triangle.

Algebra ->  Triangles -> SOLUTION: If two sides of right triangle are 5x and 3x-1. And area of triangle is 60 cm2 then find the hypotenuse of the triangle.      Log On


   

Question 807423: If two sides of right triangle are 5x and 3x-1. And area of triangle is 60 cm2 then find the hypotenuse of the triangle.
Answer by josgarithmetic(39623) About Me  (Show Source):
You can put this solution on YOUR website!
One of the sides serves as a base and the other side serves as a height.
Area is %281%2F2%29b%2Ay, where b is base, y is height.

%281%2F2%29%285x%29%283x-1%29=60 using what was given.
b=5x and y=3x-1
5x%283x-1%29=120
15x%5E2-5x=120
3x%5E2-x=24
3x%5E2-x-24=0 FACTORABLE!
%283x%2B8%29%28x-3%29=0

The positive x value has meaning here.
highlight%28x=3%29
The triangle legs are 5x=5%2A3=15 and 3x-1=3%2A3-1=8

Pythagorean Theorem gives h%5E2=15%5E2%2B8%5E2
h%5E2=289
highlight%28h=17%29


-------------------------------------
Knowing the squares of the lowest few prime numbers is a good idea.
11^2=121; 13^2=169; for 17 obviously; 19^2=361.
You'll find that your common divisibility rules give you nothing for 289, so suspect some lower prime number as a possible factor.