Question

The area of a rectangular vegetable patch is 32 square meters. The perimeter is 24 meters.
What are the dimensions of the vegetable patch?
Please help

Answer 1

Answer:

When l = 4m , breadth is 8m

When l = 8m , breadth is 4m .

Step-by-step explanation:

Here it is given that the area of a rectangular patch is 32m² . If we assume length to be l and breadth to be b , then ;

$\longrightarrow Area_{rectangle}=length\times breadth$

$\longrightarrow 32m^2 = lb \dots (i)$

Again , it's given that the perimeter is 24m .We know that perimeter of a rectangle is ,

$\longrightarrow Perimeter = 2(l+b)$

$\longrightarrow 24 = 2( l +b)$

$\longrightarrow l + b = 12\dots (ii)$

From equation (i) and (ii) , we have ;

$\longrightarrow l + \dfrac{32}{l}=12\\\\\longrightarrow \dfrac{l^2+32}{12}=1\\\\\longrightarrow l^2+32=12l \\\\\longrightarrow l^2-12l +32=0\\\\\longrightarrow l^2-4l -8l +32=0 \\\\\longrightarrow l( l -4) -8(l-4)=0\\\\\longrightarrow(l-4)(l-8)=0 \\\\\longrightarrow \underline{\underline{ l = 4,8}}$

Therefore , we can find breadth as,

$\longrightarrow l + b =12\\\\\longrightarrow b = 12 - l \\\\\longrightarrow b = 12-8, 12-4\\\\\longrightarrow \underline{\underline{b = 4,8}}$