Question

The width of a rectangle is 3 meters more than half of the length. the perimeter is 516 meters. What is the length and the width?

Answer 1

Hey there! I'm happy to help!

Let's write this out as a system of equations. We will have W be the width and L be the length.

W=0.5L+3

2L+2W=516

Since we know that W is equal to 0.5L+3, we can swap the W in the second equation with 0.5L+3 so we can solve for L!

2L+2(0.5L+3)=516

We use the distributive property to undo the parentheses.

2L+L+6=516

We combine like terms.

3L+6=516

We subtract 6 from both sides.

3L=510

We divide both sides by 3.

L=170

Now, we know that the width is 3 meters more than half the length. So, we take 1/2 of 170, which is 85, and then we add three, giving us 88.

So, our length is 170 meters and the width is 88 meters.

Have a wonderful day!

Answer 2

Length = 8 meters

Width = 5 meters

Explanation:

2*(3 + (1/4)L + L) = 26 meters

1/4L + L = 26/2 - 3

1/4L + 4/4L = 10

5/4L = 10

L = 10 * 4/5

L = 40/5 = 8 meters

W = 3 + 1/4 L

W = 3 + 1/4 *8

W = 3 + 2

W = 5 meters