Question

A cactus casts a shadow that is 15 ft long. A gate nearby casts a shadow that is 5 ft long at the same moment. If the height of the gate is 3 ft, what is the height of the cactus?

A) 9 ft
B) 5 ft
C) 7.5 ft
D) 6 ft

Answer 1

To find the height of the cactus, we can use the concept of similar triangles. By setting up a proportion between the heights and lengths of the cactus and the gate, we can solve for the height of the cactus. The height of the cactus is 9 ft.

Step-by-step explanation:

To find the height of the cactus, we can use the concept of similar triangles. Let's represent the height of the cactus as 'x'. We know that the length of the cactus's shadow is 15 ft, and the length of the gate's shadow is 5 ft. Since the cactus and the gate are in the same sunlight, we can set up the following proportion:

(Height of cactus)/(Length of cactus's shadow) = (Height of gate)/(Length of gate's shadow)

Substituting the values, we get:

(x/15) = (3/5)

Cross multiplying, we get:

5x = 45

Dividing both sides by 5, we find that the height of the cactus is:

x = 9 ft