Question

A rectangle's length is 6 more than 4 times its width. If the perimeter is 42, how long is the rectangle?

Answer 1

To find the length of the rectangle, set up an equation using the width and length. Then, solve the equation to find the width. Finally, plug the width back into the expression for the length to find its value. The length of the rectangle is 18 units.

Step-by-step explanation:

To find the length of the rectangle, we can set up an equation. Let's let the width of the rectangle be x. The problem states that the length is 6 more than 4 times the width, so the length is 4x + 6. We can set up the equation:

2(width) + 2(length) = perimeter

2(x) + 2(4x + 6) = 42

Now we can solve for x:

2x + 8x + 12 = 42

10x + 12 = 42

10x = 30

x = 3

Therefore, the width of the rectangle is 3. To find the length, we substitute x back into the expression for the length:

Length = 4x + 6 = 4(3) + 6 = 12 + 6 = 18

So, the length of the rectangle is 18 units.