Question

the hypotenuse of a right angled triangle is 1m more than twice the shortest side.If the third side is 7cm more than the shorter side,find the sides of the triangle.

Answer 1

shortest side(ab)=x
third side(bc)=x+7
diagonal(ac)=2x+1

use pythagorian theoram
ac²=ab²+bc²
(2x+1)²=(x+7)²+x²
4x²+1+4x=x²+49+14x+x²
4x²+4x+1=2x²+14x+49
2x²+4x-14x+1-49=0
2x²-10x-48=0
2x²-10x=48
x²-5x=24
x²-5x-24=0
(x-8)(x+3)=0
x=8 or x=-3

use x=8

third side=x+7=7+8=15
diagonal= 2*8+1=17

Answer 2

shortest side say(ab)=x
third side say(bc)=x+7
diagonal say(ac)=2x+1

using pythagoras theorem
ac²=ab²+bc²
(2x+1)²=(x+7)²+x²
4x²+1+4x=x²+49+14x+x²
4x²+4x+1=2x²+14x+49
2x²+4x-14x+1-49=0
2x²-10x-48=0
2x²-10x=48
x²-5x=24
x²-5x-24=0
(x-8)(x+3)=0
x=8 or x=-3

so, x=8

third side=x+7=7+8=15
diagonal= 2*8+1=17