Question

The ratio of the length to the width of the rectangle is 10:6. Of the perimeter of the rectangle is 160 meters, find the measure of the width. Show your work

Answer 1

To solve for the width of a rectangle with a length to width ratio of 10:6 and a perimeter of 160 meters, we set up a proportion, simplify the equation, combine like terms, and solve for the width. The final calculation reveals that the width of the rectangle is 30 meters.

Step-by-step explanation:

To find the measure of the width of a rectangle when the ratio of the length to the width is 10:6 and the perimeter is 160 meters, we can set up two proportions based on the given ratios and the formula for the perimeter of a rectangle, which is P = 2l + 2w (where P is the perimeter, l is the length, and w is the width).

From the given ratio of the length to width 10:6, we can say that for every 10 units of length, there are 6 units of width. We can express this as length = (10/6) × width or equivalently, width = (6/10) × length.

Using the perimeter formula, we have 160 = 2×(10/6×width) + 2×width.

Let's solve for the width:

• Simplify the equation: 160 = (20/6×width) + 2width
• To combine like terms, we first need a common denominator, so we convert 2width to (12/6)width
• Now we have 160 = (20/6 + 12/6)width
• Combine the terms: 160 = (32/6)width
• Multiply both sides by (6/32) to solve for width: width = 160 × (6/32)
• Simplify: width = 30 meters

Therefore, the measure of the width of the rectangle is 30 meters.

Answer 2

60 meters, see explanation.

Step-by-step explanation:

We know that the ratio of length : width is 10 : 6. So for every 10 meters of length, we also have 6 meters of width. This problem is much easier since we are given the P = 160 meters.

You can see that if we multiply the ratio by ten, we get 100 : 60, where 100 + 60 = 160 total meters. From here, it is clear that the width would be 60 meters.