Question

Help?? I don’t get this

Answer 1

x = 19

Explanation:

When a triangle is cut by a line parallel to its base, the resulting two triangles are similar. That means corresponding sides are proportional (their ratios are equal).

There are several ways the ratios can be written, but I like to choose one that has the variable in the numerator. Here's the proportion and its solution.

`(x+5)/(16)=(30)/(20)\\\\x+5=24\qquad\text{multiply both sides by 16}\\\\x=19\qquad\text{subtract 5 from both sides}`

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Additional comment

Technically, the corresponding sides of the triangles would be ...

• entire long side of larger triangle: ((x+5) +30) and long side of smaller triangle (30)
• entire short side of larger triangle (36) and short side of smaller triangle (20)

Since the parts labeled (x+5) and 16 are each the same fraction of their entire side, those parts are corresponding also, and will have the same proportion as other corresponding sides.