Question

If the square of the hypotenuse of an isosceles right triangle is 128 cm2, find the length of each side.​

Answer 1

⋆Solution:

Let the two equal side of right angled isosceles triangle, right angled at Q be k cm.

⋆ Given: h2 = 128

So, we get

$\small\bold{PR2 = PQ2 + QR2}$

$\small\bold{h2 = k2 + k2 }$

$\small\bold\pink{ ⇒ }\small\bold{ 128 = 2k2 }$

$\small\bold\pink{ ⇒ }\small\bold{\frac{128}{2} = k2 }$

$\small\bold\pink{ ⇒ }\small\bold{ 64 = k2}$

$\small\bold\pink{ ⇒ }\small\bold{ \sqrt{64} = k}$

$\small\bold\pink{ ⇒ }\small\bold{8 = k }$

Therefore, length of each side is 8 cm.

Answer 2

Answer:

8 cm

Step-by-step explanation:

Let the length be l.

Then, by Pythagorean Theorem,

l² + l² = 128

2l² = 128

l² = 64

l = 8 cm