A 6 ft tall tent standing next to a cardboard box cast a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it?

Answer 1

To find the height of the cardboard box, we can set up a proportion:

\(\frac{{\text{height of tent}}}{{\text{length of shadow of tent}}} = \frac{{\text{height of box}}}{{\text{length of shadow of box}}}\)

Let's plug in the values we have:

\(\frac{{6 \text{ ft}}}{{9 \text{ ft}}} = \frac{{\text{height of box}}}{{6 \text{ ft}}}\)

To solve for the height of the box, we can cross-multiply:

\(9 \times \text{height of box} = 6 \times 6\)

Simplifying that equation:

\(9 \times \text{height of box} = 36\)

Dividing both sides by 9:

\(\text{height of box} = 4\)

Therefore, the height of the cardboard box is 4 ft.