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.
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.
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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 =
It is also given that the area of the square = 64 m²
According to the question,
= 64
=> = 64 - 4
=> = 60
=> 2x = 60 * 3
=> 2x = 180
=> x =
=> 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 = m
∵ Area of rectangle = Length * Breadth
∴ 90 = y *
=> 90 =
=> 12 y² = 90 * 5
=> 2 y² = 450
=> y² =
=> y² = 225
=> y =
=> y = +15
∵Length cannot be negative,
∴ y = 15 m
∴ The length of the rectangle = 15 m
∴ The breadth of the rectangle = m
= m
=m
= 6 m