Question

1. james is designing a house that has a small roof over the porch and a larger one over the main part of the house. the diagram below represents the design of the roofs. if the triangles formed by the roofs are similar, what is the length, to the nearest foot, of x?

Explanation:

Step1: Identify similar triangles' sides

Small triangle: base=7ft, equal side=5ft; Large triangle: base=24ft, equal side=x.

Step2: Set up proportion for similarity

$\frac{7}{24} = \frac{5}{x}$

Step3: Solve for x

$x = \frac{5 \times 24}{7} = \frac{120}{7} \approx 17.14$

Step4: Round to nearest foot

$x \approx 17$

Answer:

17