Mathematics

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

  • Boy; 5ft tall: 2.5ft shadow = 5:2.5.
    Tree; x ft tall: 10ft shadow.
    10 * 5 /2.5 = 20.
    Tree is 20ft tall.
  • 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



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