# Thread: Please Help Me Explain How the Length was found in this equation

1. ## Please Help Me Explain How the Length was found in this equation

Please help me explain how the length was found in this equation. For instance a sentence or two starting out: "The length was found by..."

Thank you so much in advance!

The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. Find the length and breadth of the pool.

96m = l and w (length and width)

p = 96m (p = perimeter)
w = l / 2 + 3m
l= 30m
30 / 2m = 15 + 3m = 18 m
30l + 18w = 96p

(the answer is l = 30 and w = 18)

2. Originally Posted by littlewhitepom
Please help me explain how the length was found in this equation. For instance a sentence or two starting out: "The length was found by..."

Thank you so much in advance!

The perimeter of a swimming pool is 96m. The width is 3m more than half the length of the pool. Find the length and breadth of the pool.

96m = l and w (length and width)

p = 96m (p = perimeter)
w = l / 2 + 3m
l= 30m
30 / 2m = 15 + 3m = 18 m
30l + 18w = 96p

(the answer is l = 30 and w = 18)
P = 2l +2w

Let l = length

Let 1/2 l +3 = width

Now substitute: 2l + 2(1/2 l +3) = 96

2l +l + 6 =96

3l = 90

l = 30

Therefore, width = 1/2 l +3 = 18

3. The perimiter of the pool is 96. Call the length "L" and the width L/2+3.

The perimiter of the pool is twice the length plus twice the width. So

96=L+L+(L/2+3)+(L/2+3) OR you can write it as 96=2L+2(L/2+3)

Simplifying we get

96=2L+L+6

Rearranging and simplifying, we get

90=3L

Hence L=90/3=30

Since the width is half the length plus three, we get

W=30/2+3=18