Maths-

General

Easy

Question

# The area of rectangle is 4 times of the area of a square. The length of the rectangle is 90 cm and the breadth of the rectangle is 2/3rd of the side of the square. What is the side of the square ?

Hint:

### i. Area of a square = side2

ii. Area of a rectangle = length × breadth

## The correct answer is: ∴ Side of the given square is 15 cm.

### Step-by-step solution:-

Let the Area of the given square be x^{2} cm^{2}

∴ Area of square = x^{2} …............................................... (Equation i)

∴ side2 = x^{2} ….............................................. (Area of a square = side2)

∴ side = x ................................... (Taking square root both the sides) ................................. (Equation ii)

Now, for the given rectangle-

∴ Breadth = 2/3 × side of square ...................................... (From given information)

∴ Breadth = 2/3 × x ................................... (From Equation ii) .......................................................... (Equation iii)

Length = 90 cm ................................................................ (From given information)

Area of a rectangle = length × breadth

∴ Area of a rectangle = 90 × 2/3 × x ...................................................... (From given information & Equation iii)

∴ Area of a rectangle = 60x .......................................................................................... (Equation iv)

We are also given that-

Area of rectangle = 4 × Area of square

∴ 60x = 4 × x^{2} ................................................................. (From Equations i & iv)

∴ 60x = 4x^{2}

∴ 0 = 4x^{2} - 60x

∴ 0 = 4x (x - 15)

∴ either 4x = 0 or x - 15 = 0

∴ either x = 0 or x = 15

Since x is the side of a square, which cannot be 0, x = 15.

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