Question

a tree casts a shadow 28 m long. at the same time, the shadow cast by a 53-cm tall statue is 79 cm long. find the height of the tree. set up a proportion that solves for the height of the tree. $\frac{x}{28} = \frac{x}{79}$ $\frac{x}{y} = \frac{53}{79}$ $\frac{x}{28} = \frac{53}{79}$ $\frac{x}{28} = \frac{79}{53}$

Explanation:

Step1: Define Variables

Let \( x \) be the height of the tree (in meters, but units for proportion just need consistency in ratios). The tree's shadow is 28 m. The statue's height is 53 cm, shadow is 79 cm.

Step2: Set Up Proportion

Since at the same time, the ratio of height to shadow length should be equal for the tree and the statue. So \(\frac{\text{Tree Height}}{\text{Tree Shadow}}=\frac{\text{Statue Height}}{\text{Statue Shadow}}\), which is \(\frac{x}{28}=\frac{53}{79}\).

Answer:

\(\boldsymbol{\frac{x}{28} = \frac{53}{79}}\) (the third option)