Question

A 5-foot stick casts a shadow of 4 feet at the same time Elin casts a shadow of 4 feet 6 inches.

How tall is Elin?
a. 5 ft
b. 6 ft
C. 5 ft 7.5 inches
d. 5 ft 6 inches

Answer 1

Explanation:

this creates 2 similar triangles.

that means all angles are the same. and all the side lengths of one triangle correlate to the corresponding side lengths of the other triangle by the same multiplication factor.

4' 6" = 4.5 ft (1 ft = 12 in)

4 × f = 4.5

f = 4.5/4 = 1.125

now the same factor applies also to the relation of the heights :

5 × 1.125 = 5.625 ft

0.625 × 12 = 7.5 in (again, 1 ft = 12 in, so 0.625 ft = 7.5 in)

Elin is 5' 7.5" tall.

so, answer C is correct.