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

When l = 4m , breadth is 8m

When l = 8m , breadth is 4m .

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* 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 + (32)/(l)=12\\\\\longrightarrow (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}}`