Question

problem set 2: rectangle perimeter
2a - we do: the length of a rectangle is 3 cm less than 6 times the width. the perimeter is 54 cm. find the width and length.

Explanation:

Step1: Define variables for width/length

Let width = $w$ cm. Length $l = 6w - 3$ cm.

Step2: Use perimeter formula

Perimeter $P = 2(l + w) = 54$. Substitute $l$:
$$2((6w - 3) + w) = 54$$

Step3: Simplify the equation

Simplify inside parentheses first:
$$2(7w - 3) = 54$$
Divide both sides by 2:
$$7w - 3 = 27$$

Step4: Solve for width $w$

Add 3 to both sides:
$$7w = 30$$
$$w = \frac{30}{7} \approx 4.29$$

Step5: Calculate length $l$

Substitute $w$ into $l = 6w - 3$:
$$l = 6\times\frac{30}{7} - 3 = \frac{180}{7} - \frac{21}{7} = \frac{159}{7} \approx 22.71$$

Answer:

Width: $\frac{30}{7}$ cm (≈4.29 cm), Length: $\frac{159}{7}$ cm (≈22.71 cm)