Question

The hypotenuse of a right triangle is x cm, its one side is of length y cm and x – y = 1, then the length of the third side is (A) √1 + (B) √1 + 2 (C) √ − 2 (D) √1 + 2​

Answer 1

Step-by-step explanation:

The hypotenuse of a right triangle is x cm, its one side is of length y cm and x – y = 1, then the length of the third side is B) √1 + 2

Answer 2

Hypotenuse

Given:

A right angled triangle having hypotenuse x cm.

One side is y cm.

Equation given : $x-y=1$

To find:

length of 3rd side of the triangle.

Step-by-step explanation:

1. Write the formula of hypotenuse.
2. Use the relation given between hypotenuse and one side of triangle.
3. Solve both and find the third side.    

Calculation:

As we know that ,

$hypotenuse^{2}=base^{2}+height^{2}$

$x^{2} =y^{2}+ height^{2}$

$=> x^{2}- y^{2}=height^{2}$

$=>(x-y)(x+y)=height^{2}$

$=>x+y=height^{2}\\=>\sqrt{x+y}= height$

$=>height= \sqrt{2y+1}$

∵$( x-y=1=>x=y+1)$

Hence, the  length of the third side is $\sqrt{2x+1}$.

Hence option b will be the correct one.