The area of a rectangle and a square are the same. If the length and breadth of the rectangle are 27 cm and 3cm respectively, the side of the square is {fill _number}cm.

Question

The area of a rectangle and a square are the same. If the length and breadth of the rectangle are 27 cm and 3cm respectively, the side of the square is {fill _number}cm.

Infinity Learn · Accepted Answer

Concept- Given that, a square's area is equal to a rectangle's area. First, using the specified length and width values, we must determine the rectangle's area. We must determine the square's side values from this.
Equation used:
1. Length × breadth equals area of a rectangle
2. Square area equals

{(side)}^{2}

.
Consider the ABCD shape with length (L) and width (B)
In other words, area of rectangle ABCD = Length (L) × Breadth (B)
However, the length (L) and breadth (B) are provided as 27 cm and 3 cm, respectively, in the question.
Area of the rectangle ABCD is therefore 27×3.
Rectangle ABCD's surface area is 81

{cm}^{2}

.

Now, let's take a look at an EFGH square with side (a). Since a square has equal lengths on each of its four sides, its area can be calculated as the product of its sides.
hence, Area of a square = Let a represent the side of the square.

Therefore, the square's area is EFGH=a×a=

a^{2}

.
Give implies that the area of the rectangle equals the area of the square.
81

{cm}^{2}

=

a^{2}

, for example, where Length× Breadth =

{(side)}^{2}

The side of the square EFGH (a) is therefore

\sqrt

81

{cm}^{2}

= 9 cm.
Hence,the side of the specified square will therefore be 9 cm.

The area of a rectangle and a square are the same. If the length and breadth of the rectangle are 27 cm and 3cm respectively, the side of the square is {fill _number}cm.

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