Answer:
x = 18 (verified by algebra) ✅
Step-by-step explanation:
When we have two similar triangles, we can use a proportion to determine an unknown value.
[tex]\frac{2x + 80}{87} = \frac{80}{60}[/tex]
We will cross multiply to get two equivalent equations that can be solved.
(2x + 80) x 60 = 120x + 4800
We can simplify this by dividing both sides by 24 to get a much simpler equation to work with: 5x + 200.
80 x 87 = 6960
We will also divide this by 24. The answer is 290
5x + 200 = 290
Subtract 200
5x = 90
Divide by 5
x = 18
Now, we can also check to make sure we did everything correctly.
(2(18) + 80) x 60 = 120x + 4800
(36 + 80) x 60 = 120(18) + 4800
116 x 60 = 2160 + 4800
6960 = 6960 ✅
