Question

12/09 - similarity word problems - l
a girl 160cm tall, stands 360cm from a lamp post at night. her shadow from the light is 90cm long. how tall is the lamp post?
the height of the lamp post is \boxed{} cm.

Explanation:

Step1: Identify similar triangles

The triangle formed by the lamp post, the ground from the lamp post to the end of the shadow, and the light ray is similar to the triangle formed by the girl, her shadow, and the light ray. Let the height of the lamp post be \( h \) cm. The base of the larger triangle (lamp post's base to shadow end) is \( 360 + 90 = 450 \) cm. The base of the smaller triangle (girl's shadow) is 90 cm, and the height of the smaller triangle (girl's height) is 160 cm.

Step2: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal. So, \(\frac{h}{450}=\frac{160}{90}\).

Step3: Solve for \( h \)

Cross - multiply: \(90h = 160\times450\). Then, \(h=\frac{160\times450}{90}\). First, calculate \(160\times450 = 72000\). Then, divide by 90: \(h=\frac{72000}{90}=800\).

Answer:

800