Question

A train ticket has a perimeter of 72 centimeters and an area of 315 square centimeters. What are the dimensions of the ticket?

Answer 1

You can work out the perimeter by working out the sum of twice the length (l) and twice the width (w).

2l + 2w = 72

The area is length (l) * width (w)

l * w = 315.

Now we just need to do some rearrangement and isolate one of the terms so we can substitute it back into the area equation.

2l + 2w = 72

2l = 72 - 2w

l = 36 - w

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l * w = 315

(36 - w) * w = 315

36w - w² = 315

w² - 36w + 315 = 0

(w - 21)(w + 15) = 0

w = -15 cannot be right, because it can't be negative, so w = 21.

Now that we know the width is 21, we can substitute it into the perimeter equation to work out the length.

2l + 2w = 72

2l + 2(21) = 72

2l + 42 = 72

2l = 72 - 42

2l = 30

l = 15.

Therefore, the width is 21 cm and the length is 15 cm.