Question

Is a triangle with side lengths 20, 24, and 36 a right triangle?

Answer 1

No

Explanation:

A right angled triangle must obey Pythagoras Theorem - the square on the hypotenuse must be equal tot he sum of the squares on the other 2 sides, ie `x^2+y^2=r^2`.

In this case we get that

`20^2+24^2=976 != 36^2=1296`.

Hence Pythagoras is not satisfied and so the triangle is not right angles.

Answer 2

No

Explanation:

Remember the pythagorean theorem

If it is a right triangle:

`color(blue)(a^2+b^2=c^2`

Where `aand b` are the sides and `c` is the Hypotenuse

Remember that the Hypotenuse is the longest side of a right triangle

`:.c=36`

`rarr20^2+24^2=36^2`

`rarr400+576=1296`

`color(red)(rArr976!=1296`

So,

This is not a right triangle