Question

Help me out please. I need the answer

Answer 1

(c) 4/8 = y/14

Explanation:

You want a proportion that can be used to find the value of y in the similar triangles with sides 4, x, y and 8, 12, 14.

Corresponding sides

The side lengths of the two triangles, listed shortest to longest, are ...

• large triangle: 8, 12, 14
• small triangle: 4, x, y

The proportion used to find y must involve corresponding sides, and must involve a pair of sides whose values are known. That means (14 and y) will be involved, as will (8 and 4).

The proportion can be written 4 ways. Choice C is one of them:

`\boxed{(4)/(8)=(y)/(14)}\qquad\textbf{matches choice C}`

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Additional comment

The missing angle is (180° -100° -60°) = 20°. The shortest side is opposite the smallest angle. Since the angles are known, we can identify the order of increasing side lengths in the smaller triangle using the order of their opposite angles.

The other ways the correct proportion can be written are ...

`(8)/(4)=(14)/(y)\qquad(8)/(14)=(4)/(y)\qquad(14)/(8)=(y)/(4)`

These can be thought of as "upside down" and "sideways."

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