How to find length in quadratic equation of right angle triangle?

1 answer:

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If you have an equation you are factoring to find the length of a leg of a right triangle, factor it to solve for x. If by some chance, one of those x-values is negative we can count that one out since length will never be negative. If you have 2 positive solutions, you may have to use some math to see if both of the lengths work according to pythagorean's theorem or if only one works. It depends upon what type of information you are given other than the quadratic.

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Circle O and triangle OQR are shown below. What is the length of OQ?

zysi [14]

Answer:

Step-by-step explanation:

A circle is inscribed in an equilateral triangle PQR with centre O. If angle OQR = 30°, what is the perimeter of the triangle?

This is a circle inscribed in an equilateral triangle with side s.

If you are asking for the perimeter of PQR, it is 3s.

If you are asking for the perimeter of OQR, it is (3+23–√3)s

Since OR and SR are the hypotenuses of right triangles with adjacent side equal to ½ s, their length is ½s / cos 30° = (√3) /3.

(3/3)s + ((√3) /3)s + ((√3) /3)s = ((3 + 2√3)/3)s ≈ 2.1547s

Hope it helps