Question

A rectangular garden covers 690 square meters. The length of the garden is 1 meter more than three times its width. Find the dimensions of the gardenThe length isand the width is01(Type whole numbers.)

Answer 1

Ok, so

We got the situation here below:

We know that the area of the garden is 690 m².

So, we got that the height (1+3x) multiplied by the width (x), should be equal to 690.

`\begin{gathered} (1+3x)(x)=690 \\ x+3x^2=690 \end{gathered}`

We have to solve:

`3x^2+x-690=0`

If we solve this quadratic equation, we obtain two solutions.

One of both solutions is negative, so we will not use it.

The second one is positive and equals to 15. So, x=15.

Now that we know that x=15, we replace:

x, (Width) is equal to 15 meters.

1+3x (Length), is equal to 46 meters.

Therefore, these are the dimensions of the garden.

Width: 15 meters

Lenght: 46 meters.