Geometry Problem

Question

Determine the value of y:

Answer 1

Alright, so we have two triangles in this problem. The larger one has a height of 5 and a width of y + 2, and the smaller one has a height of 2 and a width of y. Both of these triangles have the same angle values, so they are similar. Since the triangles are similar, the ratios of their corresponding side lengths must be the same.

Setting up the ratios, we get the equation 2 / y = 5 / (y + 2). So now we just need to solve for y in this equation. Let's do this line by line.

Cross-multiply to get 2(y + 2) = 5y.

Simplify to get 2y + 4 = 5y.

Subtract 2y to get 4 = 3y.

Divide by 3 to get 4/3 = y.

So that's our answer: y = 4/3.

Answer 2

This is a straight problem in similar triangles: 2/y = 5/2.Solve this equation for y.