Question

A tree casts a 26-ft shadow. A boy stands nearby casts a 12-ft shadow, forming similar triangles. His height is 4.5 for how tall is the tree

Answer 1

9.75 ft

Since the triangles formed by the heights and shadows, the ratios of corresponding sides are equal.

the corresponding sides are the heights and the lengths of the shadows

let h be the height of the tree, then

`(h)/(4.5)` =
`(26)/(12)` ( cross- multiply )

12h = 4.5 × 26 = 117 ( divide both sides by 12 )

h = 9.75

hence the height of the tree is 9.75 ft