Question

Sara was helping her father assemble a slide for the local park. He decides to reinforce the slide with an extra support beam. How long should the extra support beam be? (Image included)

Answer 1

76.25cm

Explanation:

In the picture, we see two right triangles. The larger one has sides `122,195`, and `152`. The smaller one has sides `x, 152-57`, and the unknown hypotenuse.
We know these triangles are similar, since they both share a right angle and the corresponding angle across the right angle.

We also know the base of the smaller right triangle. We do the subtraction of `152-57` to find out that the base of the smaller right triangle is `95cm`

We can know find the ratio between the bottom base of the two right triangles.
Therefore, `95/152=x/122`
Solving this equation, we get:
`95/152=x/122`
`11590=152x`
`76.25=x`
We have the answer!