Question

1. a statue that is 12 ft tall casts a shadow that is 15 ft long. find the length of the shadow that a 8 ft cardboard box casts.

Explanation:

Step1: Set up proportion

Let $x$ = shadow length of box.
$\frac{\text{Height of statue}}{\text{Shadow of statue}} = \frac{\text{Height of box}}{\text{Shadow of box}}$
$\frac{12}{15} = \frac{8}{x}$

Step2: Simplify left fraction

Reduce $\frac{12}{15}$ to lowest terms.
$\frac{4}{5} = \frac{8}{x}$

Step3: Cross-multiply to solve for $x$

Multiply numerator of one by denominator of the other.
$4x = 5 \times 8$
$4x = 40$

Step4: Isolate $x$

Divide both sides by 4.
$x = \frac{40}{4}$
$x = 10$

Answer:

10 ft