Question

A rectangular field is ten times as long as it is wide. If the perimeter of the field is 1540 feet, what are the dimensions of the field?

Answer 1

700 by 70

Explanation:

The equation for perimeter is 2(l + w). Since the length has an assigned value, l will become 10w.

2(10w + w) = 1540

First, add the parenthetical expression to get 11w.

2(11w) = 1540

Now, DISTRIBUTE! 2(11w) becomes 22w.

22w = 1540

Lastly, divide by 22 to get 70. You can also say that this could be 22w = 154 * 10. 22 * 7 is 154 (140 + 14), and 7 * 10 is 70.

w = 70

Now that we know the width, substitute 70 for w in the 10w expression.

l = 10(70)

Just multiply and you'll get 700.

l = 700

Now we know the dimensions to be 700 * 70 (or 70 * 700; I just prefer to put the length first)