Question

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

Answer 1

Answer:

Length of side of square$=\sqrt{170}$

Step-by-step 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 $=x$

$x^{2} =12^{2}+14^{2}\\x^{2} =144+196\\x^{2} =340\\x=\sqrt{340}$

Diagonal of square $=\sqrt{340}$

let side of square$=a$

again use pythagorean theorem

$340=a^{2}+a^{a}\\2a^{2}=340\\a^{2}=170\\a=\sqrt{170}$