Question

The perimeter of a rectangle is 2(length) + 2/breadth)
The breadth of a rectangle is one-third of its length. If its perimeter is 40 cm, find its length and breath​

Answer 1

Length = 30 cm

Breadth = 10cm

Answer 2

Answer:

The answer is length $=15 \mathrm{~cm}$ and

breadth $=5 \mathrm{~cm}$.

Step-by-step explanation:

Given:

Perimeter $=40 \mathrm{~cm}$

The perimeter of a rectangle is $2 (length) +2 (breath).$

To find:

The length and breadth of the rectangle.

Step 1

The length of the rectangle be $x$

The breadth of the rectangle is $\frac{1}{3}$ of $x$

$=\frac{1}{3} * x$

$=\frac{x}{3}$

The perimeter of a rectangle $=2 a+2 b$

$=2(a+b)$

where $a$ and $b$ are length and breadth.

Step 2

Let, Perimeter $=40 \mathrm{~cm}$

then,

$&40=2\left(x+\frac{x}{3}\right)$

$&=2 x+2 \frac{x}{3}$

Consider L.C.M of the denominators 1 and $3=3$

Step 3

Now, $2 x * \frac{3}{3}$ and $\frac{2 x}{3} * \frac{1}{1}$

[To make the denominators same]

$\frac{6 x}{3}$ and$\frac{2 x}{3}$

Perimeter

$40=2 x+\frac{2 x}{3}$

$&=\frac{2 x}{3}+\frac{6 x}{3}$

$&=6 x+\frac{2 x}{3}$

$&40=\frac{8 x}{3}$

$&40 * 3=8 x \text { [By using linear equation's rules] }$

$&120=8 x$

$&x=\frac{120}{8}$

length $=15 \mathrm{~cm}$

Breadth $=\frac{x}{3}$

$=\frac{15}{3}$

Breadth $=5 \mathrm{~cm}$

Step 4

Hence,

Perimeter $=2(a+b)$

Where $a$ and $b$ are length and breadth.

Perimeter $=40 \mathrm{~cm}$

$40=2(15+5)$

$=2(20)$

$40=40$

Hence proved,

L.H.S = R.H.S

#SPJ2