Question

the area of a rectangle is 12.25sqcm greater than the area of a square of side7cm. if the breadth of tha rectangle is5cm. find its length.​

Answer 1

Answer:

Given :-

• The area of a rectangle is 12.25 sqcm greater than the area of a square of side 7 cm.
• Breadth of a rectangle is 5 cm.

To Find :-

• What is the length of a rectangle.

Formula Used :-

$\clubsuit$ Area of Square Formula :

$\mapsto \sf\boxed{\bold{\pink{Area_{(Square)} =\: (Side)^2}}}$

$\clubsuit$ Area of Rectangle Formula :

$\mapsto \sf\boxed{\bold{\pink{Area_{(Rectangle)} =\: Length \times Breadth}}}$

Solution :-

First, we have to find the area of square :

Given :

• Side = 7 cm

$\implies \sf Area_{(Square)} =\: (7\: cm)^2$

$\implies \sf Area_{(Square)} =\: 7\: cm \times 7\: cm$

$\implies \sf \bold{\purple{Area_{(Square)} =\: 49\: cm^2}}$

Now, we have to find area of rectangle :

$\mapsto$ The area of a rectangle is 12.25 cm² greater than the area of a square :

$\implies \sf Area_{(Rectangle)} =\: 49 + 12.25$

$\implies \sf Area_{(Rectangle)} =\: 49 + \dfrac{1225}{100}$

$\implies \sf Area_{(Rectangle)} =\: \dfrac{4900 + 1225}{100}$

$\implies \sf Area_{(Rectangle)} =\: \dfrac{6125}{100}$

$\implies \sf\bold{\purple{Area_{(Rectangle)} =\: 61.25\: cm^2}}$

Now, we have to find the length of a rectangle :

Let,

$\mapsto$ Length of Rectangle = x cm

Given :

• Area of Rectangle = 61.25 cm²
• Breadth of Rectangle = 5 cm

According to the question by using the formula we get,

$\longrightarrow \sf x \times 5 =\: 61.25$

$\longrightarrow \sf 5x =\: 61.25$

$\longrightarrow \sf x =\: \dfrac{\dfrac{6125}{100}}{5}$

$\longrightarrow \sf x =\: \dfrac{6125}{100} \times \dfrac{1}{5}$

$\longrightarrow \sf x =\: \dfrac{6125}{500}$

$\longrightarrow \sf\bold{\red{x =\: 12.25\: cm}}$

$\therefore$ The length of a rectangle is 12.25 cm .

Answer 2

Solution -

• The area of a rectangle is 12.25 cm² greater than the area of a square of side 7 cm .

• The breadth of the rectangle is 5 cm .

We need to find the length of this rectangle .

To start , let us assign the length of the rectangle a variable , x .

Area of the rectangle becomes -

> Length × Breadth

> 5x cm ² .

The square has a sidelength of 7 cm .

Area of the square - 49 cm²

As per the question

5x = 49 + 12.25

> 5x = 60.25

> x = 12. 05 cm .

Answer - The length of the mentioned rectangle is 12.05 cm .

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