Question

The hypotenuse of a right triangle is 6 m
more than twice the shorter side. If the third
side is 2 m less than the hypotenuse. Find the
sides of the triangle.​

Answer 1

Answer:

The sides are 10m, 24m, 26m

Step-by-step explanation:

let the shortest side of triangle be x

hypotenuse will be 2x + 6

the third side will be 2x + 6 - 2 = 2x + 4

by using Pythagoras theorem

${(2x + 6)}^{2} = {x}^{2} + {(2x + 4)}^{2} \\ 4 {x}^{2} + 24x + 36 = {x}^{2} + 4 {x}^{2} + 16x + 16 \\ 4 {x}^{2} + 24x + 36 = 5 {x}^{2} + 16x + 16 \\ 5 {x}^{2} + 16x + 16 - 4 {x}^{2} - 24x - 36 = 0 \\ {x}^{2} - 8x - 20 = 0 \\ {x}^{2} + 2x - 10x - 20 = 0 \\ x(x + 2) - 10(x + 2) = 0 \\ (x + 2)(x - 10) = 0 \\ x + 2 = 0 \: \: \: \: \: \: \: x - 10 \\ x = - 2 \: \: \: \: \: \: \: x = 10$

we take the positive value of x= 10

the sides of triangle are

x = 10

2x + 6 = 2(10) + 6 = 20 + 6 = 26

2x + 4 = 2(10) + 4 = 20 + 4 = 24

The sides are 10m, 24m, 26m

hope you get your answer