PSAT Math : How to find the perimeter of a right triangle

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #11 : Right Triangles

Three points in the xy-coordinate system form a triangle.

The points are .

What is the perimeter of the triangle?

Possible Answers:

9 + \sqrt{41}

9 + \sqrt{71}

9 + \sqrt{26}

Correct answer:

9 + \sqrt{41}


Drawing points gives sides of a right triangle of 4, 5, and an unknown hypotenuse.

Using the pythagorean theorem we find that the hypotenuse is \sqrt{41}.

Example Question #1 : How To Find The Perimeter Of A Right Triangle


Based on the information given above, what is the perimeter of triangle ABC?

Possible Answers:

Correct answer:



Consult the diagram above while reading the solution. Because of what we know about supplementary angles, we can fill in the inner values of the triangle. Angles A and B can be found by the following reductions:

A + 120 = 180; A = 60

B + 150 = 180; B = 30

Since we know A + B + C = 180 and have the values of A and B, we know:

60 + 30 + C = 180; C = 90

This gives us a 30:60:90 triangle. Now, since 17.5 is across from the 30° angle, we know that the other two sides will have to be √3 and 2 times 17.5; therefore, our perimeter will be as follows:

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