### All GMAT Math Resources

## Example Questions

### Example Question #10 : Calculating The Height Of An Acute / Obtuse Triangle

Given: with and .

Construct the altitude of from to a point on . What is the length of ?

**Possible Answers:**

**Correct answer:**

is shown below, along with altitude ; note that has been extended to a ray to facilitate the location of the point .

Since an exterior angle of a triangle has as its measure the sum of those of its remote interior angles,

By definition of an altitude, is perpendicular to , making a right triangle and a 30-60-90 triangle. By the 30-60-90 Triangle Theorem, shorter leg of has half the length of hypotenuse —that is, half of 48, or 24; longer leg has length times this, or , which is the correct choice.

### Example Question #61 : Acute / Obtuse Triangles

Given: with and .

Construct the altitude of from to a point on . What is the length of ?

**Possible Answers:**

**Correct answer:**

is shown below, along with altitude .

Since , and , by definition, is perpendicular to , is a 30-60-90 triangle. By the 30-60-90 Triangle Theorem, , as the shorter leg of , has half the length of hypotenuse ; this is half of 30, or 15.

### Example Question #62 : Acute / Obtuse Triangles

Given: with , construct two altitudes of : one from to a point on , and another from to a point on . Which of the following is true of the relationship of the lengths of and ?

**Possible Answers:**

The length of is nine-sixteenths that of .

The length of is three-fourths that of .

The length of is two-thirds that of .

The length of is four-ninths that of .

The length of is twice that of .

**Correct answer:**

The length of is three-fourths that of .

The area of a triangle is one half the product of the length of any base and its corresponding height; this is , but it is also . Set these equal, and note the following:

That is, the length of is three fourths that of that of .

Certified Tutor

Certified Tutor