Question

perimeter & area of rectangles
three rectangles are shown.
(images of three rectangles with dimensions: first 8 cm (length) and 6 cm (width), second 7 cm (length) and 8 cm (width), third 9 cm (length) and 4 cm (width))
what is the area of the rectangle that has a perimeter of 30 centimeters?
the area is \boxed{} square centimeters.

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \), where \( l \) is length and \( w \) is width. We need to find which rectangle has \( P = 30 \) cm.

Step2: Calculate Perimeter for Each Rectangle

• First rectangle: \( l = 8 \) cm, \( w = 6 \) cm.

\( P = 2(8 + 6) = 2(14) = 28 \) cm.

• Second rectangle: \( l = 8 \) cm, \( w = 7 \) cm.

\( P = 2(8 + 7) = 2(15) = 30 \) cm.

• Third rectangle: \( l = 9 \) cm, \( w = 4 \) cm.

\( P = 2(9 + 4) = 2(13) = 26 \) cm.

Step3: Calculate Area of the Correct Rectangle

The second rectangle (with \( l = 8 \) cm, \( w = 7 \) cm) has perimeter 30 cm.
Area \( A = l \times w = 8 \times 7 = 56 \) square centimeters.

Answer:

56