Question

Area of a square is 4 m² more than 2/3 of the area of a rectangle. If the area of square is 64 m² ,then find the dimensions of rectangle, given that breadth is 2/5 of length. ​

Answer 1

Answer:

Length = 15 m & Breadth = 6 m

Step-by-step explanation:

Given,

Let the area of the rectangle be x m²

∴ According to the question,

The area of the square = $(\frac{2x}{3} + 4) m^{2}$

It is also given that the area of the square = 64 m²

According to the question,

$(\frac{2x}{3} + 4)$ = 64

=> $\frac{2x}{3}$ = 64 - 4

=> $\frac{2x}{3}$ = 60

=> 2x = 60 * 3

=> 2x = 180

=> x = $\frac{180}{2}$

=> x = 90

∵ 'x' was assumed to be the value for the area of the rectangle,

∴ The area of the rectangle = 90 m²

Let the length of the rectangle be y m

∴ The breadth of the rectangle = $\frac{2y}{5}$ m

∵ Area of rectangle = Length * Breadth

∴ 90 = y * $\frac{2y}{5}$

=> 90 = $\frac{2y^{2} }{5}$

=> 12 y² = 90 * 5

=> 2 y² = 450

=> y² = $\frac{450}{2}$

=> y² = 225

=> y = $\sqrt{225}$

=> y = +15

∵Length cannot be negative,

∴ y = 15 m

∴ The length of the rectangle = 15 m

∴ The breadth of the rectangle = $\frac{2y}{5}$ m

                                                   = $\frac{2 * 15}{5}$ m

                                                   =$\frac{30}{5}$m

                                                   = 6 m

Answer 2

Answer:

Length= 15 m , Breadth = 9 m

Step-by-step explanation:

Area of square= 4+2/3 of area of rectangle = 64

4+2/3 of area of rectangle= 64

2/3 of area of rectangle= 60

Area of rectangle= 60*3/2

= 90 m²

Let length be x

Breadth = 2/5 of x

x*2/5*x = 90 m²

x² = (90*2/5) m². ( we can write 2x as x² )

x² = 225 m²

x = 15 m

Therefore Breadth = (2/5*15) m

= 9 m