Question

The perimeter of a square is 64 m.The area of a rectangle is 6 m sq less than the area of the given square.If the breadth of the rectangle is 10m.Than find its length.
a.22 m
b.31 m
c.29 m
d.25 m

Answer 1

d. 25 m

Length is 25 m

Step-by-step explanation:

Solution :

Perimeter of Square = 64m

⇒ Side × 4 = 64

⇒ Side = 64 /4 = 16 m

⇒ Side = 16 m

Area of Square = Side × Side

⇒ 16 × 16 = 256 m²

Area of Square = 256 m²

★ According to the Question :

The area of a rectangle is 6 m sq less than the area of the given square

Area of rectangle = 256 - 6 = 250 m²

Area of rectangle = 250 m²

⇒ Area of rectangle = Length × Breadth

⇒ 250m² = Length × 10 m

⇒ 250 = Length × 10

⇒ Length = 250 / 10

⇒ Length = 25 m

∴ Length is 25 m

Answer 2

Given :-

Perimeter of square = 64 m

area of a rectangle is 6 m sq. less than the area of the given square.

Length of rectangle = 10 m

To Find :-

Length of rectangle

Solution :-

At first we need to find side of square

$\sf Side = \dfrac{Perimeter}{4}$

$\sf \to Side = \dfrac{64}{4}$

$\sf \to Side = 16 \; m$

We need to find area of square

$\sf \pink{Area = side^{2}}$

$\sf \to Area = 16^{2}$

$\sf\red{Area \; = 256 \; m^{2}}$

Area of rectangle = Area of square - 6

Area of rectangle = 256 - 6

Area of rectangle = 250 m

$\sf Length = \dfrac{Area}{Breadth}$

$\sf \to Length = \dfrac{250}{10}$

$\sf \to Length = \dfrac{25}{1}$

$\sf\red{Length = 25 \; m}$

Hence,

• Length is 25 m