Question

the lengths of the sides of a rectangle are in the ratio 5:3. The perimeter of the rectangle is 32cm. Find the length of each side

Answer 1

Take x and y as the sides if the rectangle

`\begin{gathered} (x)/(y)=(5)/(3) \\ 3x=5y \end{gathered}`
`2x+2y=32`

Clear x from both equations

`\begin{gathered} x=(5)/(3)y \\ x=(32-2y)/(2)=16-y \end{gathered}`

Equal both expressions

`\begin{gathered} (5)/(3)y=16-y \\ (5)/(3)y+y=16 \\ (8)/(3)y=16 \\ y=16\cdot(3)/(8) \\ y=6 \end{gathered}`

Now find x using one of the first equations

`\begin{gathered} x=16-y \\ x=16-6 \\ x=10 \end{gathered}`

One of the sides measures 6cm and the other one 10cm