Question

38.The perimeter of a rectangle is 70 cm its length exceeds its breadth 5 cm. Find the area of the rectangle *​

Answer 1

Let the breadth ,b = x cm

Therefore, the length ,l = (x+5) cm -----(i)

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀According to the Question

☯ Perimeter Rectangle = 2(l+b)

where,

• l denote length
• b denote breadth

Substitute the value we get

$:\implies$ 70 = 2(x + x+ 5)

$:\implies$ 70 = 2(2x +5)

$:\implies$ 70 = 4x + 10

$:\implies$ 70 -10 = 4x

$:\implies$ 60 = 4x

$:\implies$ 60/4 = x

$:\implies$ x = 60/4

$:\implies$ x = 15

• breadth = 15 cm

Putting the value of x = 15 in equation (i) we get

$:\implies$ Length = 15 + 5

$:\implies$ Length = 20 cm

Now, we know that

☯ Area of rectangle = l × b

substitute the value we get

$:\implies$ Area of Rectangle = 20×15

$:\implies$ Area of Rectangle = 300 cm²

• Hence, the area of rectangle is 300 cm².

Answer 2

Answer:

Given :-

• The perimeter of a rectangle is 70 cm.
• Its length exceeds its breadth is 5 cm.

To Find :-

• What is the area of the rectangle.

Formula Used :-

$\clubsuit$ Perimeter of Rectangle :

$\longmapsto \sf\boxed{\bold{\pink{Perimeter\: Of\: Rectangle =\: 2(Length + Breadth)}}}$

$\clubsuit$ Area of Rectangle :

$\longmapsto \sf\boxed{\bold{\pink{Area\: Of\: Rectangle =\: Length \times Breadth}}}$

Solution :-

Let,

$\mapsto$ Breadth of a rectangle be x cm

$\mapsto$ Length of a rectangle will be x + 5 cm

Given :

• Perimeter = 70 cm

According to the question by using the formula we get,

$\implies \sf 2(x + x + 5) =\: 70$

$\implies \sf 2(2x + 5) =\: 70$

$\implies \sf 2x + 5 =\: \dfrac{\cancel{70}}{\cancel{2}}$

$\implies \sf 2x + 5 =\: 35$

$\implies \sf 2x =\: 35 - 5$

$\implies \sf 2x =\: 30$

$\implies \sf x =\: \dfrac{\cancel{30}}{\cancel{2}}$

$\implies \sf\bold{\green{x =\: 15\: cm}}$

Hence, the required length and breadth are :

$\dashrightarrow$ Breadth of Rectangle :

$\implies \sf x\: cm$

$\implies \sf\bold{\purple{15\: cm}}$

And,

$\dashrightarrow$ Length of Rectangle :

$\implies \sf x + 5\: cm$

$\implies \sf 15 + 5\: cm$

$\implies \sf\bold{\purple{20\: cm}}$

Now, we have to find the area of the rectangle :

Given :

• Length = 20 cm
• Breadth = 15 cm

According to the question by using the formula we get,

$\leadsto \sf Area\: of\: Rectangle =\: 20\: cm \times 15\: cm$

$\leadsto \sf\bold{\red{Area\: of\: Rectangle =\: 300\: cm^2}}$

$\therefore$ The area of the rectangle is 300 cm².