Question

question: 21 of 38
the length of a person’s shadow is proportional to their height. if a person’s shadow is 120 cm long and their height is 180 cm, how long is the shadow of a person who is 135 cm tall at the same time of day?
75 cm
160 cm
90 cm
202.5 cm

Explanation:

Step1: Define Proportional Relationship

Let \( s \) be shadow length and \( h \) be height. Since \( s \propto h \), \( \frac{s_1}{h_1} = \frac{s_2}{h_2} \). Given \( s_1 = 120 \, \text{cm} \), \( h_1 = 180 \, \text{cm} \), \( h_2 = 135 \, \text{cm} \), find \( s_2 \).

Step2: Substitute Values

Substitute into the proportion: \( \frac{120}{180} = \frac{s_2}{135} \).

Step3: Solve for \( s_2 \)

Cross - multiply: \( 180s_2 = 120\times135 \). Then \( s_2=\frac{120\times135}{180} \). Simplify: \( 120\times135 = 16200 \), \( \frac{16200}{180}=90 \).

Answer:

90 cm