Question

the figures below are similar. the labeled sides are corresponding.
4 mm
7 mm
$p_1 = 16$ mm $p_2= $?
what is the perimeter of the larger square?
$p_2 = \square$ millimeters

Explanation:

Step1: Recall perimeter of square formula

The perimeter of a square is given by \( P = 4s \), where \( s \) is the side length. For similar figures, the ratio of perimeters is equal to the ratio of corresponding side lengths.

Step2: Find the ratio of side lengths

The side length of the smaller square \( s_1 = 4 \) mm and the side length of the larger square \( s_2 = 7 \) mm. The ratio of side lengths \( \frac{s_2}{s_1}=\frac{7}{4} \).

Step3: Use perimeter ratio property

Since the ratio of perimeters of similar figures is equal to the ratio of their corresponding side lengths, let \( P_1 = 16 \) mm (perimeter of smaller square) and \( P_2 \) be the perimeter of the larger square. Then \( \frac{P_2}{P_1}=\frac{s_2}{s_1} \).

Substitute the known values: \( \frac{P_2}{16}=\frac{7}{4} \).

Step4: Solve for \( P_2 \)

Multiply both sides by 16: \( P_2 = 16\times\frac{7}{4} \).

Simplify: \( 16\div4 = 4 \), then \( 4\times7 = 28 \). So \( P_2 = 28 \) mm.

Answer:

28