Question

A rectangle with sides 12 cm and 14 cm has the same diagonal as a square.

What is the length of the side of the square.
Give your answer as a surd.​

Answer 1

Length of side of square
`=√(170)`

Explanation:

Sides of rectangle
`=12,14\ cm`

let
`x` be diagonal of rectangle

Pythagorean theorem : The square of hypotenuse is equal to sum of square of sides.

Here hypotenuse
`=x`

`x^(2) =12^(2)+14^(2)\\x^(2) =144+196\\x^(2) =340\\x=√(340)`

Diagonal of square
`=√(340)`

let side of square
`=a`

again use pythagorean theorem

`340=a^(2)+a^(a)\\2a^(2)=340\\a^(2)=170\\a=√(170)`