### All SAT Math Resources

## Example Questions

### Example Question #123 : Plane Geometry

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

The points are .

What is the perimeter of the triangle?

**Possible Answers:**

**Correct answer:**

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 .

### Example Question #124 : Plane Geometry

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:

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

Give the perimeter of the provided triangle.

**Possible Answers:**

**Correct answer:**

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 #2 : How To Find The Perimeter Of A Right Triangle

What is the perimeter of the triangle above?

**Possible Answers:**

**Correct answer:**

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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