Question

A rectangle's length is 1.5 times its width. The perimeter of the rectangle is four more than 3 times the length. What are the dimensions of the rectangle8x 126x126x98x8

Answer 1

Let l be the length of the rectangle and w be its width.

Since the length of the rectangle is 1.5 times its width, then:

`l=1.5w`

The perimeter of the rectangle is given by the expression:

`2(l+w)`

Since the perimeter of the rectangle is four more than 3 times its length, then:

`2(l+w)=4+3l`

Substitute l=1.5w into that equation and solve for w:

`\begin{gathered} \Rightarrow2(1.5w+w)=4+3(1.5w) \\ \Rightarrow2(2.5w)=4+4.5w \\ \Rightarrow5w=4+4.5w \\ \Rightarrow5w-4.5w=4 \\ \Rightarrow0.5w=4 \\ \Rightarrow w=(4)/(0.5) \\ \Rightarrow w=8 \end{gathered}`

Substitute back w=8 into the expression for l to find its value:

`l=1.5(8)=12`

Therefore, the dimensions of the rectangle are:

`8*12`