The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and width?

Question

The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and​ width?

Savannah Aguilar · Accepted Answer

Width #17# meters and the width is #40# meters.

Let the width be #x#. Then the length is #2x + 6#. We know #P = 2w + 2l#. #x + 2x + 6 + x + 2x + 6 = 114# #6x + 12 = 114# #6(x+ 2) = 114# #x+ 2 = 19# #x= 17# Because #W = 2x + 6#, #W = 2(17 + 6) = 40#. Hopefully this helps!

Theodore Abad · Answer

undefined Let's denote the width of the basketball court as $ w $ meters. According to the problem, the length is 6 meters longer than twice the width, which can be represented as $ 2w + 6 $ meters.

Given that the perimeter of the basketball court is 114 meters, we can set up the equation for the perimeter:

$$ \text{Perimeter} = 2(\text{Length}) + 2(\text{Width}) $$

Substituting the expressions for length and width:

$$ 114 = 2(2w + 6) + 2w $$

Simplify and solve for $ w $:

$$ 114 = 4w + 12 + 2w $$

$$ 114 = 6w + 12 $$

$$ 6w = 114 - 12 $$

$$ 6w = 102 $$

$$ w = \frac{102}{6} $$

$$ w = 17 $$

Now, we can find the length using $ 2w + 6 $:

$$ \text{Length} = 2(17) + 6 $$

$$ \text{Length} = 34 + 6 $$

$$ \text{Length} = 40 $$

Therefore, the width of the basketball court is 17 meters, and the length is 40 meters.

The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and​ width?

The perimeter of a basketball court is 114 meters and the length is 6 meters longer than twice the width. What are the length and width?