Question

What would be the measure of diagonal of a square whose area is equal to 578 sq cm
b) 32 cm
a) 38 cm
c) 42 cm
d) 34 cm​

Answer 1

Hey....

Option D is correct __ 34 cm...

Explanation :-

Area of square = 1/2 ( diagonal) ^2

diagonal ^2 = 2 x 578 = 1156 cm

Diagonal is √1156 = 36 cm...

Thank you

Answer 2

Given:

✰ Area of a square = 578 cm²

To find:

✠ The measure of diagonal of a square.

Solution:

Square:

A square is a rectangle with all its sides equal in length.

Area is nothing but the measure of the surface enclosed by its equal sides.

Here in this question we will use formula of area of square to calculate the side of a square. After finding the length of each side of square, we will find the measure of diagonal of square by using formulas. Putting the value in the formula and then doing the required calculations.

Let's find out...✧

✭ Area of a square = a² sq. units ✭

Where,

• a is the length of each side of a square.

Putting the values in the formula, we have:

➛ a² = 578

➛ a = √578 cm

✭ Length of the diagonal of square = √2a ✭

Where,

• a is the length of each side of a square.

Putting the values in the formula, we have:

➤ Length of the diagonal of square = √2 × √578

➤ Length of the diagonal of square = 34 cm

∴ The measure of diagonal of a square = 34 cm

_______________________________