Question

A man who is 74 inches tall stands beside a palm tree. The length of the man's shadow is 26 inches. The palm tree's shadow is 80 inches long. How tall is the palm tree? Write and solve a proportion for the unknown height.

a) The palm tree is 29 inches tall.
b) The palm tree is 92 inches tall.
c) The palm tree is 185 inches tall.
d) The palm tree is 36 inches tall.

Answer 1

To find the height of the palm tree, set up a proportion with the lengths of the man's shadow and the palm tree's shadow. Solve for x, the height of the palm tree.

Step-by-step explanation:

To find the height of the palm tree, we can set up a proportion using the lengths of the man's shadow and the palm tree's shadow. Let's let x be the height of the palm tree.

We can set up the proportion: (height of man) / (length of man's shadow) = (height of palm tree) / (length of palm tree's shadow)

Plugging in the given values, we get: 74 / 26 = x / 80

Cross multiplying, we have: 74 * 80 = 26x

Simplifying, we find: x = (74 * 80) / 26

Calculating further, we get: x = 227.69

Therefore, the height of the palm tree is approximately 227.69 inches.