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The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 98 centimeters. Find the length and width of the rectangle.

" Width "=◻" centimeters "quad" Length "=◻" centimeters "

The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is $98$ centimeters. Find the length and width of the rectangle. $\newline$ $\text { Width }=\square \text { centimeters } \quad \text { Length }=\square \text { centimeters }$

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Circles: word problems

Full solution

Q. The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is

98

centimeters. Find the length and width of the rectangle.

\newline

\text { Width }=\square \text { centimeters } \quad \text { Length }=\square \text { centimeters }

Denote Width and Length: Let's denote the width of the rectangle as $w$ and the length as $w + 1$ since they are consecutive integers. The perimeter $P$ of a rectangle is given by the formula $P = 2 \times \text{length} + 2 \times \text{width}$ .
Set Up Perimeter Equation: We know the perimeter is $98$ cm, so we can set up the equation $98 = 2(w + 1) + 2w$ .
Simplify Equation: Simplify the equation by distributing the $2$ into the parentheses and combining like terms: $98 = 2w + 2 + 2w$ which simplifies to $98 = 4w + 2$ .
Isolate Term with Width: Subtract $2$ from both sides to isolate the term with $w$ on one side: $96 = 4w$ .
Solve for Width: Divide both sides by $4$ to solve for $w$ : $w = 96 / 4$ which gives us $w = 24$ .
Find Length: Now that we have the width, we can find the length by adding $1$ to the width: $\text{length} = w + 1 = 24 + 1 = 25$ .

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