Question

the house shown below was drawn using a scale of 2 in = 5 ft. what is the actual height of the house? image of two house drawings with height labels a. 21 1/4 ft b. 21 1/4 in c. 85 ft d. 3.4 ft

Explanation:

Step1: Define scale ratio

The scale is $\frac{2\ \text{in}}{5\ \text{ft}}$, meaning 2 inches on the drawing equals 5 feet in reality.

Step2: Set up proportion

Let $x$ = actual height. Equate drawing/actual ratios:
$$\frac{2\ \text{in}}{5\ \text{ft}} = \frac{8.5\ \text{in}}{x}$$

Step3: Solve for $x$

Cross-multiply and isolate $x$:
$x = \frac{8.5\ \text{in} \times 5\ \text{ft}}{2\ \text{in}}$
$x = \frac{42.5}{2}\ \text{ft} = 21.25\ \text{ft} = 21\frac{1}{4}\ \text{ft}$

Answer:

A. $21\frac{1}{4}$ ft