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:In step 1 did Quincy make a mistakeStep-by-step explanation:Proportions states that two ratios or fractions are equal.As per the statement:Shadow of the tree = 12 ftShadow of Quincy = 3 ftHeight of the Quincy = 5 ft talllet x be the height of the tree.By definition of proportions;[tex]\frac{\text{Height of the tree}}{\text{Height of the Quincy}}=\frac{\text{Shadow of the tree}}{\text{Shadow of the Quincy}}[/tex]then;[tex]\frac{x}{5} = \frac{12}{3}[/tex]By cross multiply we have;[tex]3x = 60[/tex]Divide both sides by 3 we have;x = 20 ftSince, he made mistake in step 1.The following correct steps are:Step 1:Set up a proportion [tex]\frac{x}{5} = \frac{12}{3}[/tex]Step 2:Cross multiply [tex]3x = 12 \times 5[/tex]Step 3:Simplify:[tex]3x = 60[/tex]Step 4:Solve for x:x = 20 ft