Question

The length of a rectangle is half of its breadth, if it's perimeter is 132m, find its area?​

Answer 1

$☛Let \: the \: length \: of \: rectangle \: = > \frac{1}{2}x \\ \\☛ Let \: the \: breadth \: of \: rectangle \: = x \\ \\ ☛Perimeter \: of \: rectangle \: = > 2(l + b) \\ \\ 132 \: m \: = > 2( \frac{1}{2}x \: + x) \\ \\ 132 \: \: m \: = > 2( \frac{3x}{2} ) \\ \\ 132 \: m \: = > \cancel {2}( \frac{3x}{\cancel {2}} ) \\ \\ 132 \: m \: = > 3x \\ \\ \frac{132}{3} = > x \\ \\ ➩ \: 44 \: m \\ \\ ★ Put \: the \: value \: of \: (x = 44) \: in \: the \: length \: and \: breadth \\ \\ Length \: = > \frac{1}{2} \times 44 = > \frac{\cancel {44}}{\cancel {2}} = > 22m \\ \\ Breadth \: = > x = 44 \\ \\ Area \: of \: rectangle \: = > length \: \times breadth \\ \\ Area \: of \: rectangle \: = > \: 22m \: \times 44m \\ \\ ❝Area \: of \: rectangle \: = >968\: {m}^{2}❞$

Answer 2

Answer:

The area of a rectangle is $968 m^2$.

Step-by-step explanation:

In context to the question asked,

We have to find the area of a rectangle,

As per the data given in the question,

We have,

Perimeter is $132m$,

A rectangle's length equals half of its breadth.

Let, the length of a rectangle = $\frac{1}{2}x$

The breadth of a rectangle = $x$

As we know that,

The perimeter of the rectangle = $2 [ l + b ]$

Now, substitute the values in the above formula,

=> $132 m = 2 [ \frac{1}{2} x+x]$

Solving the terms in the brackets,

=> $132 m = 2 [ \frac{3x}{2}]$

Canceling out 2, we get

=> $132 m = 3x$

Divide both sides by 3, we get

=> $44m=x$

So, the value of x is 44m.

Now, substitute the value of x in the length and the breadth.

Length = $\frac{1}{2}x$

$= >\frac{1}{2} \times 44$

$=>22m$

Breadth = $x = 44m$

For calculating the area,

The formula to be used:-

Area of a rectangle = l $\times$ b

$=> 22\times 44$

$=> 968 m ^2$

So, the area of a rectangle is $968 m^2$.