Question

At 1:00 pm, Abby stands next to her house and measures her shadow and the house's shadow. Abby is 5 ft tall, and her shadow is 3 ft long. The house's shadow is 14 ft long. How tall is the house?

Answer 1

To find the height of the house, we can set up a proportion using Abby's height and the lengths of their respective shadows. By cross multiplying and simplifying the equation, we can determine that the height of the house is approximately 23.33 feet.

Step-by-step explanation:

In this problem, we can set up a proportion to find the height of the house. Since Abby's height and her shadow form a proportion with the length of her shadow and the length of the house's shadow, we can write the following equation:

Abby's Height / Abby's Shadow Length = House's Height / House's Shadow Length

Substituting the given values:

1. Abby's Height = 5 ft
2. Abby's Shadow Length = 3 ft
3. House's Shadow Length = 14 ft

Plugging in these values, the equation becomes:

5 ft / 3 ft = House's Height / 14 ft

Cross multiplying:

3(ft) x House's Height = 5(ft) x 14(ft)

House's Height = (5(ft) x 14(ft)) / 3(ft)

Simplifying the equation:

House's Height = 70(ft) / 3(ft)

House's Height ≈ 23.33 ft

Therefore, the height of the house is approximately 23.33 feet.