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horrorfan [7]
3 years ago
5

Which of the following can be the side lengths of a triangle?

Mathematics
1 answer:
dolphi86 [110]3 years ago
3 0
To solve this question, we need to know the triangle inequality property, which states that the sum of two legs of a triangle is always <em>greater </em>(it can't be equal to) than the third leg. Using this property, we can deduct that the only answer that works is A, 6,6, and 5. 
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$ PS = \frac{4}{3} x

Solution:

Given PRQ is a triangle.

ST is a line parallel to RQ.

$PT = x, \ PQ = 3x,  \ SR=\frac{8}{3}x

TQ=PQ-PT

TQ=3x -x=2x

<u>Triangle proportionality theorem,</u>

<em>If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.</em>

$\frac{PS}{SR} =\frac{PT}{TQ}

$\frac{PS}{\frac{8}{3} x} =\frac{x}{2x}

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