Question

the lenght of the rectangle is 1½ times it's breadth.If the perimeter of the rectangle is 100m.find the area of the rectangle.​

Answer 1

Given :-

• The length of the rectangle is 1½ times it's breadth.

• The perimeter of the rectangle is 100m.

To Find :-

• Find the area of the rectangle.

Solution :-

~Here, we’re given the information about the length and breadth of a rectangle and also it’s perimeter. Firstly we’ll find the length and the breadth by applying the formula of perimeter and then of area.  

• Let the Breadth of rectangle b ‘x’  

• Then the length will be ‘1½x’ or ‘3x/2’  

As we know that ,  

$\sf \maltese \;\; Perimeter\;of\;rectangle = 2(l+b)$

$\sf \maltese \;\; Area\;of\;rectangle = lb$

Where,  

• l is length  

• b is breadth

Finding the length and breadth :-  

$\sf \implies 100 = 2 \bigg\{ \dfrac{3x}{2} + x } \bigg \}$

$\sf \implies 100 = 2 \bigg\{ \dfrac{3x+2x}{2} \bigg\}$

$\sf \implies 100 = 2 \bigg\{ \dfrac{5x}{2} \bigg\}$

$\sf \implies 100 = 2 \times \dfrac{5x}{2}$

$\sf \implies 5x = 100$

 

$\sf \implies x = \dfrac{100}{5}$

$\sf \implies x = 20$

_________________

$\sf \leadsto Length = 30\;m$

$\sf \leadsto Breadth = 20\;m$

_________________

Finding the area :-

$\sf \implies 20\;m \times 30\;m$

 

$\sf \implies 600\;m^{2}$

Hence,  

• Area of the rectangle is 600 m