Question

A flight of stairs is supported by two columns as shown in the diagram. What is the distance from the base of the stairs to the taller column?

Answer 1

The base of the larger triangle is 12 feet. The calculation is based on the ratio of corresponding sides of similar triangles, which in this case is the ratio of the base to the hypotenuse for both the smaller and the larger triangle.

The problem involves finding the base of a larger triangle, given the hypotenuse of both the smaller and the larger triangles, as well as the base of the smaller triangle. This can be solved by using the properties of similar triangles. The triangles are similar because they are both right-angled and share an angle, meaning all their angles are the same.

We are given:

- Base of the smaller triangle = 4 feet

- Hypotenuse of the smaller triangle = 6 feet

- Hypotenuse of the larger triangle = 18 feet

We need to find:

- Base of the larger triangle

To find the base of the larger triangle, we will use the fact that the ratio of the corresponding sides of similar triangles is constant. The formula for the ratio is:

`\( \frac{\text{base of smaller triangle}}{\text{hypotenuse of smaller triangle}} = \frac{\text{base of larger triangle}}{\text{hypotenuse of larger triangle}} \)`

Let's denote the base of the larger triangle as
`\( b \)`.

So, we can set up the equation as:

`\( (4)/(6) = (b)/(18) \)`

Now we can solve for
`\( b \)`. Let's do the calculation.

`b=12`

The base of the larger triangle is 12 feet. The calculation is based on the ratio of corresponding sides of similar triangles, which in this case is the ratio of the base to the hypotenuse for both the smaller and the larger triangle.

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