Question

A child's playhouse is built to look like a smaller version of the family house, where the ends of the roofs have similar proportions. The width of the main house is 32 feet and the length from the peak to the gutter of the roof for one of the sides is 20 feet. If the width of the playhouse is 12 feet, what is the length from the peak to the gutter of the playhouse roof?

A. 8 feet
B. 15 feet
C. 7.5 feet
D. 6 feet

Answer 1

The correct length is c)7.5 feet.

Step-by-step explanation:

The question is asking us to calculate the proportional length from the peak to the gutter of the playhouse roof based on the similar proportions of the family house and the playhouse. Since similar figures have proportional dimensions, we can set up a proportion using the width and length from peak to gutter of each structure to find the unknown length of the playhouse roof.

To solve this, we set up the proportion as follows:

Width of main house / Length from peak to gutter of main house = Width of playhouse / Length from peak to gutter of playhouse

32 feet / 20 feet = 12 feet / x feet

Now we cross multiply and solve for x:

32x = 12 × 20

32x = 240

x = 240 / 32

x = 7.5 feet

Therefore, the length from the peak to the gutter of the playhouse roof is 7.5 feet, which corresponds to option C.