To solve this problem, we have the following information:

1. Perimeter of the rectangle: 154 feet
2. Ratio of length to width: 10:1

Let:

• $L$ be the length of the rectangle.
• $W$ be the width of the rectangle.

From the ratio 10:1, we can express $L$ in terms of $W$ as: $L = 10W$

The formula for the perimeter of a rectangle is: $P = 2(L + W)$

Substitute the given perimeter (154 feet) and $L = 10W$ into the formula: $154 = 2(10W + W)$

Simplify inside the parentheses: $154 = 2(11W)$

Now, divide both sides by 2: $77 = 11W$

Divide by 11 to isolate $W$: $W = 7 \text{ feet}$

Now, substitute $W = 7$ back into $L = 10W$ to find the length: $L = 10 \times 7 = 70 \text{ feet}$

Solution:

• Width (W) = 7 feet
• Length (L) = 70 feet

Would you like further details on the steps, or have any questions?

Here are 5 related questions for further practice:

1. If the ratio of length to width was 5:1 and the perimeter was 84 feet, what would be the length and width?
2. For a rectangle with a length-to-width ratio of 8:1 and perimeter of 160 feet, find the dimensions.
3. If the perimeter of a rectangle is doubled but the ratio remains the same, how do the dimensions change?
4. Given a perimeter of 120 feet and length-to-width ratio of 3:1, calculate the dimensions.
5. If a rectangle has a length of 50 feet and the width is one-fifth of the length, what is the perimeter?

Tip: When given a ratio, express one variable in terms of the other to simplify the problem.