Question

question 4
the length of a rectangle is two feet less than three times the width. the perimeter is 44 feet. find the width w by solving the equation 2w + 2(3w − 2) = 44.
the width is
feet.
check answer

question 5
2 pts 1 details
the length of a rectangle is two inches more than eight times the width. the perimeter is 58 inches. find the length and width.
the length is
inches, and the width is
inches.
check answer

Explanation:

Question 4

Step1: Simplify the left side

First, expand \(2(3W - 2)\) using the distributive property: \(2\times3W - 2\times2 = 6W - 4\). Then the equation becomes \(2W + 6W - 4 = 44\). Combine like terms: \(8W - 4 = 44\).

Step2: Solve for W

Add 4 to both sides: \(8W - 4 + 4 = 44 + 4\), so \(8W = 48\). Divide both sides by 8: \(W=\frac{48}{8}=6\).

Step1: Define variables and perimeter formula

Let the width be \(w\) inches. Then the length \(l = 8w + 2\) inches. The perimeter of a rectangle is \(P = 2(l + w)\), and \(P = 58\), so \(2((8w + 2)+w)=58\).

Step2: Simplify and solve for w

Simplify inside the parentheses: \(2(9w + 2)=58\). Distribute: \(18w + 4 = 58\). Subtract 4: \(18w = 54\). Divide by 18: \(w = 3\).

Step3: Find the length

Substitute \(w = 3\) into \(l = 8w + 2\): \(l = 8\times3 + 2 = 26\).

Answer:

6

Question 5