Question

11. Length of a rectangle is 16 cm less than twice its breadth. If the perime of rectangle is 100 cm, find its length and breadth.​

Answer 1

Given :

• Length of a rectangle is 16 cm less than twice its breadth.
• If the perimeter of rectangle is 100 cm.

To Find:

• Length and breadth

Solution:

Let,

• Breadth of Rectangle = x cm
• Length of Rectangle = (2x - 16) cm

Perimeter of Rectangle = 2 (L + B)

➠ 100 = 2 (x + 2x - 16)

➠ 100 = 2 (3x - 16)

➠ 100 = 6x - 32

➠ 6x = 132

➠ x = 132/6

➠ x = 22cm

Now,Finding Length and breadth

Length of Rectangle = 2x - 16

• Length of Rectangle = 2 × 22 - 16
• Length of Rectangle = 28cm

Breadth of Rectangle = x cm

• Breadth of Rectangle = 22cm

Answer 2

$\frak{Given}= \begin{cases} &\sf{Length\:of\:a\:rectangle\:is\:16\:cm\:less\:than\:twice\:its\:breadth\:.} \\\\\\\\\\\\ &\sf{The\:perimeter\:of\:rectangle\:is\:100 cm.}\end{cases}$

To find:-  

• Length
• Breadth

Assume:-  

• Breadth of Rectangle = x cm

• Length of Rectangle = (2x - 16) cm

Solution:-  

$\qquad\sf{:\implies\:\:Perimeter\:_{(Rectangle)}\:=\:2\:(\:Lenght\:+\:Breadth\:)}$

$\qquad\sf{:\implies\:100\:=\:2\:(\:x\:+\:2x\:-16\:)}$

$\qquad\sf{:\implies\:100\:=\:2\:(\:3x\:-16\:)}$

$\qquad\sf{:\implies\:100\:=\:6x\:-\:32\:}$

$\qquad\sf{:\implies\:100\:+\:32=\:6x\:\:}$

$\qquad\sf{:\implies\:132\:=\:6x}$

$\qquad\sf{:\implies\:x\:=\:\dfrac{132}{6}}$

$\qquad\sf{:\implies\:x\:=\:22}$

Length:-  

$\qquad\sf{:\implies\:Length\:_{(Rectangle)}\:=\:2x\:-\:16}$

$\qquad\sf{:\implies\:Length\:_{(Rectangle)}\:=\:2\:\times\:22\:-\:16}$

$\qquad\sf{:\implies\:Length\:_{(Rectangle)}\:=\:44\:-\:16}$

$\qquad\sf{:\implies\:Length\:_{(Rectangle)}\:=\:28cm}$

$\color{lime}{\sf{\underline{Therefore\:the\:Length\:of\:the\:rectangle\:is\:28cm\:.}}}$

Breadth:-  

$\qquad\sf{:\implies\:Breadth\:_{(Rectangle)}\:=\:X\:cm}$

$\qquad\sf{:\implies\:Breadth\:_{(Rectangle)}\:=\:22cm\:.}$

$\color{pink}{\sf{\underline{Therefore\:the\:Bredth\:of\:the\:rectangle\:is\:22cm\:.}}}$