Question

Quincy is trying to estimate the height of a tree in his backyard. He measures the tree’s shadow as 12 ft. He stands near the tree and measures his own shadow as 3 ft. Quincy knows that he is about 5 ft tall. He estimates the height of the tree by following these steps: Step 1: Set up a proportion x 12 = 3 5 Step 2: Cross multiply 5x = 12 × 3 Step 3: Simplify 5x = 36 Step 4: Solve for x x = 7.2 feet In which step, if any, did Quincy make a mistake?

Answer 1

Quincy made a mistake in Step 1. The correct proportion is actually

`(x)/(12)` =
`(5)/(3)` .

Answer 2

In step 1 did Quincy make a mistake

Explanation:

Proportions states that two ratios or fractions are equal.

As per the statement:

Shadow of the tree = 12 ft

Shadow of Quincy = 3 ft

Height of the Quincy = 5 ft tall

let x be the height of the tree.

By definition of proportions;

`\frac{\text{Height of the tree}}{\text{Height of the Quincy}}=\frac{\text{Shadow of the tree}}{\text{Shadow of the Quincy}}`

then;

`(x)/(5) = (12)/(3)`

By cross multiply we have;

`3x = 60`

Divide both sides by 3 we have;

x = 20 ft

Since, he made mistake in step 1.

The following correct steps are:

Step 1:

Set up a proportion

`(x)/(5) = (12)/(3)`

Step 2:

Cross multiply

`3x = 12 * 5`

Step 3:

Simplify:

`3x = 60`

Step 4:

Solve for x:

x = 20 ft