Question

One leg of a right-angled triangle is 1 cm less and the other one is 8 cm
less than the hypotenuse. Find the hypotenuse.

Answer 1

Answer:

let the hypotenuse is x cm

then one side (x-1) cm

other side =(x-8)cm

so,

(x-1)^2+(x-8)^2=x^2

=> x^2-2x+1+x^2-16x+64=x^2

=> 2x^2-18x+65-x^2=0

=> x^2-18x+65=0

=> x^2-13x-5x+65=0

=> x(x-13)-5(x-13)=0

=> (x-13)(x-5)=0

=> x-13=0

=> x=13

x-5=0

=> x=5

x can not be 5 cm because one side is 8 cm less than hypotenuse

so hypotenuse is 13 cm

Answer 2

Answer:

the hypotenuse will be 13cm

it won't be 5cm as one side is already 8cm less than hypotenuse and when we substitute value as 5 answer will be negative and length cannot be negative