Question

the hypotenuse of a right triangle is 25cm. the difference between the lengths of the other two sides of the triangle is 5cm. find the lengths of these sides.

Answer 1

Let the sides of a triangle be x and (x+5)

We know that,

By Pythagoras Theorem,

(25)^=x^ + (x+5)^

625=x^ + x^ +10x +25

2x^ + 10x -600=0

x^ +20x -15x -300=0

(x +20)(x -15)=0

x= -20 and x=15

Since length can never be negative,

Therefore, x=15

Also, other side will be=x +5=15 +5=20

Hence the sides of the triangles are 15 and 20

Answer 2

Let the length of the shorter side be x cm.

Then, the length of the shorter side = (x+5) cm

By Pythagoras theorem,

${x }^{2} + (x + 5) ^{2} = {25}^{2}$

$⇒ \: {x}^{2} + {x}^{2} + 10x + 25 = 625$

$⇒ \: 2 {x}^{2} + 10x - 600 = 0$

$⇒ \: {x}^{2} + 5x - 300 = 0$

$⇒ \: (x + 20)(x - 15) = 0$

This gives x = 15 or x = - 20

Rejecting x = -20, we get x = 15

$\fbox\bold{Length \: of \: Shorter \: side = 15 cm}$

$\fbox \bold{Length \: of \: Longer \: side = 20 cm}$