Question

1. kaylee is 100 cm tall and is standing so that her mother’s shadow covers her shadow. she is 90 cm from her mother and her mother’s shadow is 225 cm long. how tall is her mother? express your answer to the nearest centimetre.

Explanation:

Step1: Find Kaylee's shadow length

Kaylee is 90 cm from her mother, and the mother's shadow is 225 cm long. So Kaylee's shadow length is \( 225 - 90 = 135 \) cm.

Step2: Set up proportion for similar triangles

Let \( h \) be the mother's height. Since the triangles are similar, the ratios of height to shadow length are equal: \( \frac{h}{225} = \frac{100}{135} \)

Step3: Solve for \( h \)

Multiply both sides by 225: \( h = \frac{100 \times 225}{135} \)
Calculate: \( h = \frac{22500}{135} \approx 166.67 \)

Step4: Round to nearest centimetre

\( 166.67 \approx 167 \)

Answer:

167 cm