I still don't understand this precalculus question

Question

I need some help on precalculus

Pizzeria Buonapetito makes a triangular-shaped pizza with base width of 30 inches and height 20 inches as shown. Alice wants only a portion of the pizza and does so by making a vertical cut through the pizza and taking the shaded portion. Letting x be the bottom length of Alice’s portion and y be the length of the cut as shown, answer the following questions:

(a) Find a formula for y as a multipart function of x, for 0 ≤ x ≤ 30.

(b) Find a formula for the area of Alice’s portion as a multipart function of x, for 0 ≤ x ≤ 30

(c) If Alice wants her portion to have half the area of the pizza, where should she make the cut?

Answer 1

The picture doesn't match with the description in the question.

I assume base=30 inches (10 in and 20 in from the left vertex to the right) and the height is 20 in.

(a), (b)

1) In the first picture,

If 0≤x≤10, the shaded triangle is similar to the triangle base 10 and height 20, so

x:y=10:20, x/y=1/2 ∴y=2x, Area=1/2(xy)=1/2(x⋅2x)=x²

2) In the second picture,

If 10<x≤30, the non-shaded triangle is similar to the triangle base 20 and height 20, so

(30-x):y=20:20, (30-x):y=1 ∴y=30-x,

Area=Total area-(non-shaded area)=1/2(20⋅30)-1/2(30-x)y=300-1/2(30-x)(30-x)=300-1/2(30-x)²

(b) To get the half of the slice, x should be more than 10 (picture 2)

Half =1/2⋅1/2(20⋅30)=150

300-1/2(30-x)²=150, x=30-10√3 since x≤30.