Question

A square measures 15 cm on each side. Its area is greater than thrice the area of a rectangle whose one side measures 10cm. What is the longest possible length of the other side of the rectangle?

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answer with solution

Answer 1

Given data :

• A square measures 15 cm on each side.
• Area of square is greater than thrice the area of a rectangle whose one side measures 10cm.

To find : The longest possible length of the other side of the rectangle ?

Solution :

Here, according to given,

→ {Area of square} = 3 * {Area of rectangle}

We know,

→ Each side of square = 15 cm

Hence, by formula of area of square

→ Area of square = ( side )²

→ Area of square = ( 15 )²

→ Area of square = 225 cm² .....( 1 )

Now, according to given,

Let, length of the rectangle be 10 cm.

→ Area of rectangle = length * breadth

→ Area of rectangle = 10 * breadth

{ Here, we take, breadth = B }

→ Area of rectangle = 10 * B ......( 2 )

Now,

→ {Area of square} = 3 * {Area of rectangle}

[from ( 1 ) & ( 2 )]

→ 225 = 3 * {10 * B }

→ 225 = 10 * B

→ 225/3 = 10 * B

→ 75 = 10 * B i.e.

→ B = 75/10

→ B = 7.5 cm

Answer : Hence, the longest possible length of the other side of the rectangle is 7.5 cm.

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