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.

Question

asked Feb 25, 2024 210k views

1 Answer

Lei Shi · Answer 1 · 2024-03-01T10:15:10+0000

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.