Question

(iv) The length of sides of a right-angled triangle are (x-2) cm, x cm and (x+2) cm. How
much length of hypotenuse is?​

Answer 1

Answer:

Hypotenuse = 10 cm

Step-by-step explanation:

According to Pythagoras Theorem,

H² = P² + B²

(x+2)² = (x-2)² + (x)²                        [Hypotenuse is (x+2) as it's the longest]

x² + 4 + 4x = x² + 4 - 4x + x²          [(a+b)² = a²+b²+2ab & (a-b)² = a²+b²-2ab]

4x = -4x + x²                                   (Cancelling Common terms)

8x = x²

8 = x                                               (ANS.)

If x = 8 cm, then (x-2) = 6 cm and (x+2) = 10 cm.

Thus, length of the hypotenuse of the triangle is 10 cm.

HOPE YOU ARE CLEAR...!!!

Answer 2

Step-by-step explanation:

by compairing, simply we can say that x+2 is greatest so x+2 is hypotenuse

now , hypotenuse^2= base^2+perpendicular^2

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

x^2+4+4x = x^2 + x^2+4-4x

4x= x^2 -4x

8x = x^2

x=8

(Using Pythagoras theorem)

so hypotenuse is x+2= 8+2=10 cm