Question

area of a square is 4 square metre more than 2 by 3 of the area of the rectangle if the area of the square is 64 square metre then find the dimensions of the rectangle given that breath is 2 by fifth of the length​

Answer 1

Let the length of the rectangle be x

Breadth of the rectangle = 2/5 of length = 2/5 * x = 2x/5

Area of the rectangle = Length × Breadth

= x × 2x/5

= 2x²/5

Area of the rectangle = 2x²/5

Area of the square = 64 m²

Given : 4 m² more than the 2/3 of Area of rectangular = Area of the square

$\frac{2}{3}( \frac{2 {x}^{2} }{5}) + 4 = 64$

$\frac{4 {x}^{2} }{15} + 4 = 64$

$\frac{4 {x}^{2} }{15} = 64 - 4$

$\frac{4 {x}^{2} }{15} = 60$

$4 {x}^{2} = 60 \times 15$

$4 {x}^{2} = 900$

${x}^{2} = \frac{900}{4}$

${x}^{2} = 225$

$x = \sqrt{225}$

$x = 15$

Therefore length of the rectangle = x = 15 m

Breadth of the rectangle = 2x/5 = 2(15)/5 = 30/5 = 6 m