Question

The length of a rectangle is 23 cm less than 6 times it's width. it's area is 35 square centimeters. find the dimensions of the rectangle use the formula,area equal length times width.

Answer 1

We are given that the area of a rectangle is 42 square meters. The formula for the area of a rectangle is:

`A=wl`

Where "w" is the width and "l" is the length. We are also told that the width is 5 meters longer than one-third of the length, this can be written mathematically as:

`w=(1)/(3)l+5`

Replacing in the formula for the area:

`A=((1)/(3)l+5)l`

Now we use the distributive property:

`A=(1)/(3)l^2+5l`

Now we replace the value of the area:

`42=(1)/(3)l^2+5l`

Now we subtract 42 to both sides:

`(1)/(3)l^2+5l-42=0`

Now we can multiply both sides by 3:

`l^2+15l-126=0`

Now we factor this equation, we need two numbers which sum is 15 and their product is 126, we get:

`(l+21)(l-6)=0`

Now we set each factor to zero:

`\begin{gathered} l+21=0 \\ l=-21 \end{gathered}`
`\begin{gathered} l-6=0 \\ l=6 \end{gathered}`

We take the positive value and therefore, the length of the rectangle is 6 meters.

To determine the width we use the relationship given by the problem:

`w=(1)/(3)l+5`

Replacing l = 6:

`\begin{gathered} w=(1)/(3)(6)+5 \\ w=2+5 \\ w=7 \end{gathered}`

The width is 7 meters.