Question

In a right angle triangle if the sum of the squares of the sides making a right angle is 289 then what is the lenth of the hypotenuies​

Answer 1

Given:

• Sum of squares of side making right angle is 289.

To Find:

• What is the length of hypotenuse ?

Solution: 

Let ABC be a right angled triangle at B in which

AB = Perpendicular

BC = Base

AC = Hypotenuse

∠ABC = 90°

Pythagoras Theorem : It states that sum of the squares of two side containing the right angle is always equal to square of the third side i.e hypotenuse.

Applying Pythagoras Theorem in ∆ABC

★ H² = B² + P² ★

⟹ AC² = AB² + BC²

⟹ 289 = AB² + BC²

⟹ 289 = AC²

⟹ √289 = AC

⟹ √17 × 17 = AC

⟹ 17 = AC

________________________

Hence, the length of hypotenuse of triangle is 17 cm.

________________________

Answer 2

Answer:

As we know that according to Pythagoras theorem, Sum of the square of two sides containing right angles is always equal to square of the third side that is also hypotenuse. Hence, the length of third side = 13.

As per the question,

We have been provided that the sum of the squares of the sides making right angle is 169.

As we know that according to Pythagoras theorem,

Sum of the square of two sides containing right angles is always equal to square of the third side that is also hypotenuse.

If PQR is the right triangle at ∠Q = 90°

∴ PQ² + QR² = PR²

Using this concept, we can find the value of third side

PQ² + QR² = PR²

169 = PR²

∴ PR = 13

Hence, the length of third side = 13.