Question

the two legs of a right angle are equal in length and the square of the length of its hypotenuse is 162 square metre centimetre find the length of each leg

Answer 1

Lets use pythagoras theorem:

a square + b square = c square

we don't know the a and b sides but we know the hypotenuse
so:

a square + b square = 162 square

we have got a hint that the legs of the triangle are of equal length so:
let the side of triangle be x
so:

x square + x square = 162 square

so, 2x square =162 square
       x square = 162square/2
        x square = 81 square
        x  = square root of 81
       x  = 9
so each side of angle is 9