Question

An arch in the shape of a parabola is 1 foot wide at its base and 25 feet tall. How wide is the arch 9 feet up?

A. 5ft
B. 4ft
C. 9ft
D. 8ft

Answer 1

The width of the arch 9 feet up from the base is approximately 0.36 feet.

Step-by-step explanation:

To find the width of the arch 9 feet up, we can use similar triangles. The height of the arch is 25 feet, and the width at the base is 1 foot. Let's set up a proportion:

Height of arch / Width of arch = Height above 9 feet / Width above 9 feet

25 feet / 1 foot = Height above 9 feet / Width above 9 feet

Now, we can solve for the width above 9 feet:

Width above 9 feet = Height above 9 feet x Width of arch / Height of arch

Plugging in the values, we get:

Width above 9 feet = 9 feet x 1 foot / 25 feet = 9/25 = 0.36 feet

Therefore, the width of the arch 9 feet up is approximately 0.36 feet.