Question

the breath of rectangular plot is 20 m less than it's length find the dimensions if it's perimeter is 120 m ​

Answer 1

Given:-

• The breadth of a rectangular plot is 20 m less that its length
• Perimeter = 120 m

To find:-

• The dimensions (length and breadth)

Answer:-

❖ As it is given that, the breadth is 20 m less the length,

▪Let the length of the rectangular plot be x metres.

▪Then the breadth will be (x - 20) m

❖ It is also given that, the plot is rectangular. We know that, for a rectangle,

$\dag \underline{\boxed{\blue{\bf{ 2(l + b) = P}}}}$ where P is perimeter, l is length and b is breadth of the rectangle.

But it is given that, Perimeter = P = 120 m

So, putting the values according to the question,

$\sf \: 2(l + b) = P$

$\longrightarrow \sf 2\{x + (x - 20) \} = 120 \: m$

$\longrightarrow \sf x + (x - 20) = \dfrac{120}{2} \: m$

$\longrightarrow \sf 2x - 20= 60 \: m$

$\longrightarrow \sf 2x = 60 + 20 \: m$

$\longrightarrow \sf 2x = 80 \: m$

$\longrightarrow \sf x = \dfrac{80}{4} \: m$

$\longrightarrow \sf x = 40 \: m$

So,

• Length = x = 40 metres
• Breadth = x - 20 = (40 - 20) m = 20 metres