Question

solve the problem by setting up and solving an appropriate algebraic equation. suppose that the length of a certain rectangle is 7 meters less than four times its width. the perimeter of the rectangle is 56 meters. find the length and width of the rectangle length m width enter an exact number m resources ebook

Explanation:

Step1: Define variables

Let the width of the rectangle be $w$ meters. Then the length $l = 4w - 7$ meters.

Step2: Write the perimeter formula

The perimeter $P$ of a rectangle is given by $P=2(l + w)$. We know that $P = 56$ meters. Substitute $l = 4w-7$ into the perimeter formula: $56=2((4w - 7)+w)$.

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $56=2(4w - 7+w)=2(5w - 7)$. Then distribute the 2: $56 = 10w-14$.

Step4: Solve for $w$

Add 14 to both sides of the equation: $56 + 14=10w-14 + 14$, which gives $70 = 10w$. Divide both sides by 10: $w=\frac{70}{10}=7$ meters.

Step5: Solve for $l$

Substitute $w = 7$ into the length formula $l = 4w-7$. So $l=4\times7 - 7=28 - 7 = 21$ meters.

Answer:

length: 21 m
width: 7 m