A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft long. The triangle shown for the tree and its shadow is similar to the t
Mathematics
lorraineshuler
Question
A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft long. The triangle shown for the tree and its shadow is similar to the triangle shown for the boy and his shadow. If the boy is 5 ft tall, how tall is the tree?
2 Answer

1. User Answers m1ax0x0
Boy; 5ft tall: 2.5ft shadow = 5:2.5.
Tree; x ft tall: 10ft shadow.
10 * 5 /2.5 = 20.
Tree is 20ft tall. 
2. User Answers OrethaWilkison
Answer:
As per the statement:
Shadow of tree = 10 ft
Shadow of boy = 2.5 ft
and
height of the boy = 5 ft
we have to find the height of the tree.
Since, the given triangles are similar their corresponding sides are in proportions
then;
[tex]\frac{\text{Shadow of tree}}{\text{Shadow of boy}} = \frac{\text{Height of tree}}{\text{Height of boy}}[/tex]
Substitute the given values;
[tex]\frac{10}{2.5} = \frac{\text{Height of tree}}{5}[/tex]
Multiply both sides by 5 we have;
[tex]\text{Height of tree} = \frac{10}{2.5} \times 5 = \frac{100 \cdot 5}{25}= 4 \cdot 5 = 20[/tex]
Therefore, the height of the tree is , 20 ft