Question

The length of a rectangle is 5cm longer than its width and its area is 66 cm2 . Find the perimeter of the rectangle.

Answer 1

Step-by-step explanation:

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Answer 2

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

The length of a rectangle is 5 cm longer than it's width and its area is 66 cm².

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The perimeter of the rectangle.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

Let the width of rectangle be r cm

Let the length of rectangle be (r+5) cm

Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(8,2)\thicklines\put(7.7,3){\large{A}}\put(7.5,2){\large{(r+5)cm}}\put(7.7,1){\large{B}}\put(9.5,0.7){\sf{\large{r\:cm}}}\put(11.1,1){\large{C}}\put(8,1){\line(1,0){3}}\put(8,1){\line(0,2){2}}\put(11,1){\line(0,3){2}}\put(8,3){\line(3,0){3}}\put(11.1,3){\large{D}}\end{picture}$

We know that formula of the area of rectangle :

$\boxed{\bf{Area=Length\times breadth}}}}$

A/q

$\longrightarrow\sf{(r+5)(r)=66}\\\\\longrightarrow\sf{r^{2} +5r=66}\\\\\longrightarrow\sf{r^{2} +5r-66=0}\\\\\longrightarrow\sf{r^{2} +11r-6r-66=0\:\:\:[factorise]}\\\\\longrightarrow\sf{r(r+11)-6(r+11)=0}\\\\\longrightarrow\sf{(r+11)(r-6)=0}\\\\\longrightarrow\sf{r+11=0\:\:Or\:\:r-6=0}\\\\\longrightarrow\sf{\orange{r\neq -11\:\:\:Or\:\:\:r=6}}$

Thus;

The length of the rectangle = (6+5)cm = 11 cm

The width of the rectangle = 6 cm

Now;

$\boxed{\bf{Perimeter\:of\:rectangle=2(Length+breadth)}}}}$

$\longrightarrow\sf{Perimeter=2(11 +6)cm}\\\\\longrightarrow\sf{Perimeter=2(17)\:cm}\\\\\longrightarrow\sf{\orange{Perimeter=34\:cm}}$

Thus;

$\dag\:\underbrace{\sf{The\:perimeter\:of\:rectangle=34\:cm}}}$