Question

In right angled triangle, if sum of the sides making right angle is 169, then what is the length of the hypotenuse ​

Answer 1

Answer:

$\large\bold\red{ h = \sqrt{ {b}^{2} - 338b + 28561 } }$

Step-by-step explanation:

Let in the right angled triangle,

• Perpendicular length = p
• Base length = b
• Hypotenus length = h

Given,

Sum of sides making right angle is 169.

We know that,

Perpendicular and base make the right angle .

Therefore,

We get,

$= > p + b = 169 \\ \\ = > p = 169 - b\: \: \: \: .......(1)$

Also,

We know that,

$\large\boxed{\bold\purple{ {p}^{2} + {b}^{2} = {h}^{2}}}$

Substituting the values,

We get,

$= > {h}^{2} = {(169 - b)}^{2} + {b}^{2} \\ \\ = > {h}^{2} = {(169)}^{2} + {b}^{2} - 338b \\ \\ = > {h}^{2} = {b}^{2} - 338b + 28561 \\ \\ = > \bold{ h = \sqrt{ {b}^{2} - 338b + 28561 } }$