Question

an architect is designing a ramp with a height of 2 meters and a horizontal extension of 6 meters. calculate the ramp length.
a. 6.00
b. 6.20
c. 6.32
d. 6.54
in the context of this lesson, what does the term \space diagonal\ refer to?
a. the longest diagonal inside a 3d shape
b. the height of a prism
c. the width of a base
d. the perimeter of a base

Explanation:

Step1: Identify the problem type

This is a right - triangle problem (ramp forms a right - triangle).

Step2: Apply Pythagorean theorem

The height of the ramp is one leg ($a = 2$), the horizontal extension is the other leg ($b = 6$), and the ramp length $c$ is the hypotenuse. The Pythagorean theorem is $c=\sqrt{a^{2}+b^{2}}$.

Step3: Calculate

$c=\sqrt{2^{2}+6^{2}}=\sqrt{4 + 36}=\sqrt{40}\approx6.32$.

For the second question:

In 3D shapes, the space diagonal is the longest diagonal that can be drawn inside the shape, connecting non - adjacent vertices.

Answer:

For the first question: c. 6.32
For the second question: a. The longest diagonal inside a 3D shape