Question

What should be the measure of the diagonal of a square whose area is 162cm^2

Answer 1

area of square ==> 162cm^2

area of square ===> 1/2 × (diagonal)^2
162 ===> 1/2 × (diagonal)^2
162 × 2 ===> diagonal^2

324 ===> diagonal ^2
18cm ===> diagonal

Answer 2

Answer:

The length of diagonal is 18 cm.

Step-by-step explanation:

$\text{Given the area of square }162cm^2\text{. we have to find the measure of diagonal.}$

$\text{The area of square is }a^2$

where a is the edge of square.

$\text{The diagonal of square is }\sqrt2a$

Squaring both sides, we get

$D^2=2a^2$

$d^2=2A$

As area=162 square centimeter

$d^2=2A=2\times 162$

$d=18 cm$

The length of diagonal is 18 cm.