Question

6. The length and width of a rectangular field are in the ratio 3:2. If the area of the field is 150 square units find its perimeter

Answer 1

\[l=3a\]\[w=2a\]where length is l, and width is w. You can see then that length to width is\[\frac{l}{w}=\frac{3a}{2a}=\frac{3}{2}\]
You know\[A=lw \]so\[150=(3a)(2a)=6a^2\]That is\[a^2=\frac{150}{6}=25\]so\[a=\pm 5\]Since we're dealing with length and width, we take the positive solution only (i.e a=5). So, the perimeter is\[p+2l+2w=2(3a)+2(2a)=10a=10(5)=50\]units.

Answer 2

^^ \[p=2l+2w\]