Question

hashim is 5 feet and 2 inches tall. his shadow is 124 inches. using his height and shadow lengths, create a similar triangle to calculate the length of a shadow of a 20 - foot tree. (1 point)
120 inches or 10 feet
480 inches or 40 feet
240 inches or 20 feet
360 inches or 30 feet
check answer remaining attempts : 3

Explanation:

Step1: Convert Hashim's height to inches

Since \(1\) foot \( = 12\) inches, Hashim's height is \(5\times12 + 2=62\) inches.

Step2: Set up the proportion for similar triangles

Let \(x\) be the length of the tree's shadow (in inches). The proportion is \(\frac{\text{Hashim's height}}{\text{Hashim's shadow}}=\frac{\text{Tree's height}}{\text{Tree's shadow}}\). The tree's height is \(20\times12 = 240\) inches. So \(\frac{62}{124}=\frac{240}{x}\).

Step3: Solve the proportion

Cross - multiply: \(62x=124\times240\). Then \(x=\frac{124\times240}{62}\). Since \(124\div62 = 2\), \(x = 2\times240=480\) inches. Convert \(480\) inches to feet: \(480\div12 = 40\) feet.

Answer:

480 inches or 40 feet