Question

What is the length of side of an isosceles right angled triangle whose hypotenuse is 42cm?​

Answer 1

Answer:

21√2

Step-by-step explanation:

An isosceles right triangle is a right triangle with two legs equal in length and has angles of 45∘ − 45∘ − 90 ∘ .

By Pythagorean Theorem, we know that,

hypotenuse

⇒ c² = a² + a ²

⇒c² = 2a

⇒c = √2a

where c is the hypotenuse and a is the leg

So for an isosceles right triangle with side length a , the hypotenuse has a length of a√2 .

Similarly, if the hypotenuse of an isosceles right triangle has length of a , the legs have a length of $\sf \: \frac{a}{ \sqrt{2} } \: \: or \: \: \frac{ a \sqrt{2} }{2}$ each.

Given that the hypotenuse of the isosceles right triangle = 42,

$\sf \: ⇒ the \: length \: of \: each \: leg \: = \frac{42}{ \sqrt{2} } = 21 \sqrt{2}$

Check ;

$⇒ \sf(21 \sqrt{2}) {}^{2} + {(21 \sqrt{2} )}^{2}$

$⇒ \sf \: (882) + (882)$

$⇒ \sf \: 1764$

Root value be 42