Question

70. The length of a rectangle is 5/3 parts of its breadth. If perimeter of rectangle is 80
metre, then area of the rectangle is?
A. 48 m²
B. 66.6 m²
C. 375 m²
D. 400 m²​

Answer 1

Answer :-

• Option c is correct.
• The area of the rectangle is 375 m².

To find :-

• The area of the rectangle.

Step-by-step explanation :-

Let the breadth of the rectangle be "x" m.

It has been given that :-

• The length of the rectangle is 5/3 of it's breadth.

Hence,

$\rm The \: length \: will \: be \: \dfrac{5}{3} \times x = \dfrac{5x}{3} \: m.$

------------------------------------

• Before finding the area of the rectangle, let's find it's dimensions first!

We know that :-

$\underline{\boxed{\sf Perimeter \: of \: a \: rectangle= 2 \: (L+ B)}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = "5x/3" m.
• Breadth = "x" m.

• Perimeter = 80 m.

Substituting the given values in this formula,

$\tt 80 = 2 \: \left(\dfrac{5x}{3} + x\right)$

The LCM of 3 and 1 is 3, so adding the fractions using their denominators,

$\tt 80 = 2 \: \left(\dfrac{5x \times 1 + x \times 3}{3} \right)$

On simplifying,

$\tt 80 = 2\: \left(\dfrac{5x + 3x}{3} \right)$

Adding 5x to 3x,

$\tt 80 = 2 \: \left(\dfrac{8x}{3}\right)$

Removing the brackets,

$\tt 80 = 2 \times \dfrac{8x}{3}$

Multiplying 2 with 8x/3,

$\tt 80 = \dfrac{16x}{3}$

Transposing 3 from RHS to LHS, changing it's sign,

$\tt 80 \times 3 = 16x$

Multiplying 80 with 3,

$\tt 240 = 16x$

Transposing 16 from RHS to LHS, changing it's sign,

$\tt \dfrac{240}{16} = x$

Dividing 240 by 16,

$\overline{\boxed{\tt 15 \: m = x}}$

------------------------------------

Hence, the dimensions of the rectangle are as follows :-

$\bf Breadth = x = 15 \: m.$

$\bf Length = \dfrac{5x}{3} = \dfrac{5 \times 15}{3} = \dfrac{75}{3} = 25 \: m.$

------------------------------------

• Now finally let's find the area of the rectangle!

We know that :-

$\underline{\boxed{\sf Area \: of \: a \: rectangle = L \times B}}$

Where,

• L = Length.
• B = Breadth.

Here,

• Length = 25 m.
• Breadth = 15 m.

Hence,

$\rm Area = 25 \times 15$

$\rm Area = 375 \: m^2$

________________________________

• The area of the rectangle is 375 m².
• So option c is correct.