Question

100 Points! Geometry question. Find x and y. Please show as much work as possible. Photo attached. Thank you!

Answer 1

Answer: x=2, y=4

Explanation:

Since the lines are parallel, we can say that the larger triangle and the smaller triangle are similar. Thus. x+3/(2y-1) = (3/2x+2)/(3y-5). Also, note that there are hash lines, telling us that 2y-1 and 3y-5 are equal. Thus 2y-1=3y-5, and y=4. Plugging y=4 into the first equation yields: (x+3)/(7)=(3/2x+2)/(7), or x+3=3/2x+2. Then 1/2x=1, x=2.

Thus: x=2, and y=4

Answer 2

x = 2

y = 4

Explanation:

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

As the line bisects the side of the triangle with the y-variables, then the line is the midsegment of the triangle. This means that the line also bisects the side of the triangle with the x-variables.

Therefore, the two expressions with the x-variable are equal.

Similarly, the two expressions with the y-variable are equal.

Solving for x:

`\boxed{\begin{aligned}(3)/(2)x+2&=x+3\\\\(3)/(2)x+2-x&=x+3-x\\\\(1)/(2)x+2&=3\\\\(1)/(2)x+2-2&=3-2\\\\(1)/(2)x&=1\\\\2 \cdot (1)/(2)x&=2 \cdot 1\\\\x&=2\end{aligned}}`

Solving for y:

`\boxed{\begin{aligned}3y-5&=2y-1\\\\3y-5-2y&=2y-1-2y\\\\y-5&=-1\\\\y-5+5&=-1+5\\\\y&=4\end{aligned}}`