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

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #172 : 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{26}

9 + \sqrt{41}

9 + \sqrt{71}

Correct answer:

9 + \sqrt{41}

Explanation:

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 #175 : Triangles

Triangle

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

Possible Answers:

Correct answer:

Explanation:

Triangle-solution

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:

Example Question #41 : Geometry

Right triangle 7

Give the perimeter of the provided triangle.

Possible Answers:

Correct answer:

Explanation:

The figure shows a right triangle. The acute angles of a right triangle have measures whose sum is , so

Substituting  for :

This makes  a 45-45-90 triangle.

By the 45-45-90 Triangle Theorem, legs  and  are of the same length, so

.

Also by the 45-45-90 Triangle Theorem, the length of hypotenuse is equal to that of leg  multiplied by . Therefore, 

.

The perimeter of the triangle is 

Example Question #42 : Geometry

Right triangle 7

What is the perimeter of the triangle above?

Possible Answers:

Correct answer:

Explanation:

The figure shows a right triangle. The acute angles of a right triangle have measures whose sum is , so

Substituting  for :

This makes  a 45-45-90 triangle. By the 45-45-90 Triangle Theorem, the length of leg  is equal to that of hypotenuse , the length of which is 12, divided by . Therefore,

Rationalize the denominator by multiplying both halves of the fraction by :

By the same reasoning, .

The perimeter of the triangle is 

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