Question

Compute the distance between points A and B and enter it on the worksheet.

Answer 1

The calculated distance between points A and B is 22 inches

How to determine the distance between points A and B

From the question, we have the following parameters that can be used in our computation:

The figure

Where, we have that

The parallel lines under the stairs are congruent

This means that

The line parallel to the 11 inches line equals to 11 inches

Using the above as a guide, we have the following:

AB = 11 inches + 11 inches

Evaluate

AB = 22 inches

Hence, the distance between points A and B is 22 inches

Answer 2

AB = 22 inches

BC = 21 inches

DC = 56.1 inches

Explanation:

We can assume that the height (rise) and depth (tread) of each step of the staircase is the same. (See attachment).

So, the distance between points A and B is:

`\sf AB=2 * 11\; inches = 22\; inches`

The distance between points B and C is:

`\sf BC=3 * 7\; inches = 21 \;inches`

Triangle BCD is a right triangle where:

• m∠B = 90°
• BC = 21 inches
• DB = 30 inches + 22 inches = 52 inches

Since triangle BCD is a right triangle, we can calculate the distance between points D and C (hypotenuse) using Pythagoras Theorem:

`\boxed{\begin{array}{l}\underline{\sf Pythagoras \;Theorem} \\\\\Large\text{$a^2+b^2=c^2$}\\\\\textsf{where:}\\\phantom{ww}\bullet\;\textsf{$a$ and $b$ are the legs of the right triangle.}\\\phantom{ww}\bullet\;\textsf{$c$ is the hypotenuse (longest side) of the right triangle.}\\\end{array}}`

As BC and DB are the legs of the right triangle, and DC is the hypotenuse, then:

`BC^2+DB^2=DC^2`

Substitute the values for BC and DB, then solve for DC:

`21^2+52^2=DC^2`

`441+2704=DC^2`

`DC^2=3145`

`DC=√(3145)`

`DC=56.08029957...`

`DC=56.1\; \sf inches\;(nearest\;tenth)`

Therefore, the distance between points D and C is 56.1 inches (rounded to the nearest tenth).