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6.12: Rectangle Facts

Difficulty Level: At Grade Created by: CK-12
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Rectangle Facts - Apply formulas

Teacher Notes

Each problem gives facts about the relationship between the length and the width of a rectangle, and its perimeter. Students use facts and the formula for the perimeter of a rectangle to determine the dimensions of the rectangle. Once the dimensions of the rectangle are determined, students figure out the area of the rectangle.

Solutions

  1. Length 10 inches, Width 2 inches, Area 20 square inches
  2. Length 8 inches, Width 5 inches, Area 40 square inches
  3. Length 9 inches, Width 5 inches, Area 45 square inches
  4. Length 8 inches, Width 3 inches, Area 24 square inches
  5. Length 12 inches, Width 4 inches, Area 48 square inches
  6. Length 8 inches, Width 7 inches, Area 56 square inches

\begin{align*}& \mathbf{Describe} && \text{The length of the rectangle is 5 inches greater than its width. Its}\\ &&& \text{perimeter is 26 inches.}\\ & \mathbf{My \ Job} && \text{Use the facts about the rectangle. Figure out its length and width in}\\ &&& \text{inches.}\\ &&& \text{Then find the area of the rectangle}\\ & \mathbf{Plan} && \text{Draw a rectangle and label the sides} \ c \ \text{and} \ d. \ \text{Since the length is}\\ &&& \text{greater than the width, draw the rectangle to show this.}\\ &&& \text{Use the facts to figure out the values of} \ c \ \text{and} \ d.\\ &&& \text{Figure out the area.}\\ & \mathbf{Solve} && \text{From the facts the length}\\ &&& \text{is} \ 5 \ \text{more than} \ c.\\ &&& \text{So show the width as} \ c.\\ &&& \text{Show the length as} \ c + 5.\\ &&& \text{Perimeter:} \ c + c + 5 + c + c + 5 = 26. \\ &&& \text{So} \ 4c + 10 = 26, \ \text{and} \ 4c = 26 - 10, \ \text{or} \ 16, \ \text{and} \ c = 4 \ \text{inches.}\\ &&& \text{Then} \ d = c + 5, \ \text{so} \ d = 4 + 5, \ \text{or} \ 9 \ \text{inches.}\\ &&& \text{The area of Rectangle} \ A \ \text{is} \ 4 \times 9, \ \text{or} \ 36 \ \text{square inches.}\end{align*}

\begin{align*}{\;} \qquad \qquad \mathbf{Check} \qquad P: 4 + 9 + 4 + 9 = 26; \ A: 4 \times 9 = 36\end{align*}

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