Question

Isabelle, who is 62 inches tall, is standing beside a tree and casts a 93 inch shadow on the ground. The shadow of the tree she is standing next to is 279 inches long, but she does not have a ladder to measure the height of the tree. Use a ratio to find the height of the tree. Draw a representation of the problem.​

Answer 1

Given:

Height of Isabelle = 62 inches

Shadow of Isabelle = 93 inches

Shadow of tree = 279 inches

To find:

The height of the tree.

Solution:

Let height of tree be x.

Ratio of height to shadow for Isabelle and tree are

$\dfrac{\text{Height of Isabelle}}{\text{Shadow of Isabelle}}=\dfrac{62}{93}$

$\dfrac{\text{Height of tree}}{\text{Shadow of tree}}=\dfrac{x}{279}$

The shadow of Isabelle and tree are proportional to their shadows. So, both ratios must be equal.

$\dfrac{x}{279}=\dfrac{62}{93}$

Multiply both sides by 279.

$x=\dfrac{62}{93}\times 279$

$x=62\times 3$

$x=186$

Therefore, the height of tree is 186 inches.