Question

plz give a step by step solution for above question.

Answer 1

Step-by-step explanation:

short side=x

hypotenuse=6+2x

third side=6+2x-2=4+2x

2 2 2

(6+2x) = x. +(4+2x)

2 2 2

36+4x+24x=x +16+4x+16x

2

20+8x=x

2

x-8x-20=0

(x+2)(x-10)

x cant be negative so x=10

hypotenuse=6+2x=6+2*10=26cm

Answer 2

Answer:

26 cms

Step-by-step explanation:

Let the hypotenuse of the triangle be 'x'

Let the shortest distance be 'y' and the other side be 'z'

According to the question,  

x = 6 + 2y and

z = x - 2 = 6 + 2y - 2= 4 + 2y

Applying Pythagoras Theorem,

x² = y² + z²

(6 + 2y)² = y² + (4 + 2y)²

Applying (a+b)² = a² + 2ab + b²,

6² + 2*6*2y + (2y)² = y² + 4² + 2*4*2y + (2y)²

36 + 24y + 4y² = y² + 16 + 16y + 4y²

4y² - y² - 4y² +24y - 16y = -36 + 16

-y² + 8y = -20

-y² + 8y + 20 =0

y² - 8y + 20 =0

y² - 10y  + 2y - 20 =0

y ( y - 10) + 2 ( y - 10) = 0

(y - 10) * (y + 2) = 0

⇒ y - 10 = 0  or y + 2 = 0

⇒y = 10 or y = -2

As y cannot be a negative integer, y = 10

Using y = 10 in x = 6 + 2y, we get

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

∴ The length of the hypotenuse is 26 cms