Question

A rectangles is 25 m long and 16 m broad find the side if a square whose area is equal to the area of this rectangle

Answer 1

Answer:

Area of the square =(25×25) cm

2

=625 cm

2

∴ Area of the rectangle =(625−125) cm

2

=500 cm

2

∴ Breadth of the rectangle =

Length

Area

=

25

500

cm=20cm

Answer 2

Given:

• the length of the rectangle = 25 m
• the breadth of a rectangle = 16 m
• the area of the rectangle = the area of the square

To find:

• the length of the side of the square

Solution:

→ Let us find the area of the rectangle whose length and breadth are given.

Area of a rectangle = length x breadth

Area of this rectangle = 25 m x 16 m

                                    = 400 m²

Since the area of the rectangle is equal to that of the square, 400 m² is the area of the square too.

→ Now, we find the area of the square.

Area of a square = side squared

So, the length of the side = √area

The side of the square of area 400 m² = √400

Let us find the square root of 400 by prime factorization:

$\Large \begin{array}{c|c} \underline{\sf {2}}&\underline{\sf {\; \; 400 \; \; \: }} \\ \underline{\sf {2}}&\underline{\sf {\; \; 200 \; \; \: }}\\ \underline{\sf {2}}&\underline{\sf {\; \; 100 \; \; \: }} \\ \underline{\sf {2}}&\underline{\sf {\; \; 50 \; \; \: }} \\ \underline{\sf {5}}&\underline{\sf {\; \; 25 \; \; \: }} \\ \underline{\sf {5}}&\underline{\sf {\; \; 5 \; \; \: }} \\ & {\sf \; 1 \; \; }\end{array}$

400 = 2 x 2 x 2 x 2 x 5 x 5

       = (2 x 2 x 5)²

       = 20²

The side of the square of area 400 m² = √400 = 20

Therefore, the side of the square is 20 m.

Mensuration Formulas

These are some formulas to find the area and perimeter of common shapes:

• Triangle

Perimeter: side₁ + side₂ + side₃

Area: 1/2 × base × height

• Square

Perimeter: 4 × side

Area: side²

• Rectangle

Perimeter: 2 × (l + b)

Area: l × b

• Circle

Circumference: 2πr

Area: πr²