Question

The length if a rectangle is 5cm more than its breadth. If the perimeter is 30 cm, find the length and breadth of the rectangle?

Answer 1

Question -

The length of a rectangle is 5 cm more than its breadth. If the perimeter is 30 cm, find the length and breadth of the rectangle?

Solution -

Let the breadth(b) of the rectangle be x

Then length(l) of the rectangle will be x+5

Now,

We know that,

Perimeter of rectangle =2(l+b)

Now putting the values we will get

$30 = 2(x + 5 + x)$

$30 = 2(2x + 5)$

$30 = 4x + 10$

$4x = 30 - 10$

$4x = 20$

$x = \frac{20}{4}$

$x = 5$

Therefore the length of the rectangle =(5+5)cm=10cm

and breadth of the rectangle =5 cm

Answer 2

☯ Let Breadth of Rectangle be x cm.

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\boxed{\bf{\mid{\overline{\underline{\bigstar\: According\: to \: the \: Question :}}}}\mid}$

Length of Rectangle is 5 cm more than its breadth.

Therefore,

Breadth of Rectangle is (5 + x) cm

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\linethickness{0.4mm}\put(7.7,3){\large\sf{A}}\put(7.3,2){\sf{\large{x cm}}}\put(7.7,1){\large\sf{B}}\put(9.1,0.7){\sf{\large{(x + 5) cm}}}\put(11.1,1){\large\sf{C}}\put(11.1,3){\large\sf{D}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\end{picture}$

We know that,

$\star\;{\boxed{\sf{\purple{Perimeter_{(rectangle)} = 2(l + b)}}}}$

$:\implies\sf 2(x + 5 + x) = 30$

$:\implies\sf 2(2x + 5) = 30$

$:\implies\sf 2x + 5 = \cancel{ \dfrac{30}{2}}$

$:\implies\sf 2x + 5 = 15$

$:\implies\sf 2x = 15 - 5$

$:\implies\sf 2x = 10$

$:\implies\sf x = \cancel{ \dfrac{10}{2}}$

$:\implies{\boxed{\frak{\pink{x = 5}}}}\;\bigstar$

Therefore, Dimensions of rectangle is,

Breadth, x = 5 cm

Length, x + 5 = 5 + 5 = 10 cm

$\therefore\;{\underline{\sf{Dimensions\;of\;rectangle\;(length\;and\;breadth)\;is\;5\;cm\;and\;10\;cm\; respectively.}}}$