Question

the length of a rectangle is 5 m less than 3 times the width and the area of the rectangle is 28 m squared. find the dimensions of the rectangle

Answer 1

let

w = width

l = length

l = 3w - 5

`\text{area}=lw`
`\begin{gathered} \text{area}=w(3w-5) \\ 28=3w^2-5w \\ 3w^2-5w-28=0 \end{gathered}`
`\begin{gathered} 3w^2+7w-12w-28=0 \\ w(3w+7)-4(3w+7)=0 \\ (w-4)(3w+7)=0 \\ w=4 \end{gathered}`

width = 4 m

length = 3(4) - 5 = 12 - 5 = 7 m