Question

If the length of the rectangle is 13 times the width and the area is 39m^2 ,then find the measure of both of the dimensions.​

Answer 1

Hello!

Answer:

`\boxed{\sf Width = √(3) , ~~Lenght = 13√(3) }`

Explanation:

Let the width of the rectangle be x. So:

Width = x

Lenght = 13x

We know that the area of the rectangle is equal to 39m².

The area of the rectangle is equal to:

`\sf A = l * w = 13x * x = 13x^2`

So, now, we have this equation:

`\sf 13x^2 = 39`

Let's solve this equation to find the measure of both of the dimensions of the rectangle.:

▪ First, divide both sides by 13:

`\sf (13x^2 )/(13) = (39 )/(13)`

Simplify:

`\sf x^2 = 3`

▪ Finally, calculate the square root of both sides:

`\sf √(x^2) = √(3)`

Simplify:

`\sf x = √(3)` because a lenght is always > 0.

So:

Width = √3

Lenght = 13√3

Conclusion:

The width of the rectangle is √3 meters and the length of the rectangle is 13√3 meters.