SOLUTION: a garden has the shape of a right triangle with one leg 8 meters longer than the other. The hypotenuse is 5 meters less than twice the length of the shorter leg. what is the length

Algebra ->  Triangles -> SOLUTION: a garden has the shape of a right triangle with one leg 8 meters longer than the other. The hypotenuse is 5 meters less than twice the length of the shorter leg. what is the length      Log On


   

Question 536390: a garden has the shape of a right triangle with one leg 8 meters longer than the other. The hypotenuse is 5 meters less than twice the length of the shorter leg. what is the length of the shorter leg
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
One leg =x
other leg = x+8
Hypotenuse = 2x-5
By Pythagoras theorem
(2x-5)^2=x^2+(x+8)^2
4x^2-20x+25=x^2+x^2+16x+64
2x^2-36x-39=0
Find the roots of the equation by quadratic formula

a= 2 ,b= -36 c -39

b^2-4ac= 1296 - 312
b^2-4ac= 1608
sqrt%28%091608%09%29= 40.1
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=( 36 + 40.1 )/ 4
x1= 19.02
x2=( 36 -40.1 ) / 4
x2= -1.025
Ignore negative value
shorter length = 19.02m
m.ananth@hotmail.ca