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

Answer:

$a=\sqrt{170}$

Step-by-step explanation:

Diagonal of a Square

Given a square of length side a, the length of the diagonal is

$D=\sqrt{2}a$

The diagonal of a rectangle of sides x and y is

$D=\sqrt{x^2+y^2}$

The sides have lengths 12 cm and 14 cm, the diagonal is

$D=\sqrt{12^2+14^2}$

$D=\sqrt{340}$

Since this value is the same of the diagonal of certain square, we can say

$\sqrt{2}a=\sqrt{340}$

Dividing by $\sqrt{2}$

$\boxed{a=\sqrt{170}}$