Question

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

Answer 1

L=p/2-W

Step-by-step explanation:

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Answer 2

Answer:

The answer is length $=15cm$ and

breadth$=5cm$.

Step-by-step explanation:

Given:

Perimeter $= 40 cm$

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

To find:

The length and breadth of the rectangle.

Step 1

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 $= 2a + 2b$

$= 2(a + b)$

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

Step 2

Let, Perimeter $= 40 cm$

then,

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

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

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

Step 3

Now, $2x *\frac{3}{3}$ and $\frac{2x}{3}* \frac{1}{1}$ [To make the denominators same]

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

(Perimeter) $40= 2x + \frac{2x}{3}$  

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

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

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

$40 * 3 = 8x$ [By using linear equation's rules]

$120 = 8x$

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

length $= 15 cm$

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

$= \frac{15}{3}$

$=5cm$

Step 4

Hence,

Perimeter = 2(a + b)

Where a and b are length and breadth.

Perimeter $= 40 cm$

$40 = 2(15 + 5)$

$= 2(20)$

 $40 = 40$

Hence proved,

$L.H.S = R.H.S$

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