Question

the measure of two adjacent sides of the rectangle are in the ratio of 11.10 if the perimeter of rectangle is 84 cm , find its area

Answer 1

$\huge\mathfrak{\underline{\underline{Answer:-}}}$

Let the sides of the rectangle be 11x and 10x

Perimeter of a rectangle = 2(l+b)

= 84 cm

According to the problem ,

2(11x + 10x) = 84

22x + 20x = 84

42x = 84

x = 84/42

x = 2

One side - 11×2 = 22cm (length)

Another side - 2×10 = 20cm(breadth)

Area = L × B

= 22 cm × 20 cm

= 440 square centimetre

(Answer)

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Area of the rectangle = 440 cm²

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :-

• The measure of two adjacent sides of the rectangle are in the ratio of 11:10
• Perimeter of rectangle is 84 cm

To find :-

• Area of the rectangle

Solution :-

Let x be the common multiple of the ratio 11:10

•°•The adjacent sides =11x & 10x.

Length (l) = 11x cm

Breadth (b) = 10x cm

Perimeter = 84 cm

Using the formula for Perimeter of a rectangle we will further deal with this question.

$\bold{Perimeter\:of\:a\:rectangle\:=\:2\:(l\:+\:b})$

Substitute the values,

$\implies$ $\bold{84\:=\:2\:(11x\:+\:10x)}$

$\implies$ $\bold{84\:=\:22x\:+\:20x}$

$\implies$ $\bold{84\:=\:42x}$

$\implies$ $\bold{x\:=\frac{84}{42}}$

$\implies$ $\bold{x\:=\:2\:}$

Substitute x = 2 for length and breadth of the rectangle,

Length = 11x = 11 × 2 = 22 cm

Breadth = 10x = 10 × 2 = 20 cm

Now we can easily calculate the area of the rectangle using the formula.

$\bold{Area\:of\:rectangle\:=\:length\:\times\:breadth}$

$\implies$ $\bold{Area\:=\:22\times\:20}$

$\implies$ $\bold{Area\:=\:440\:sq.cm}$