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?
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.