How to find the height of a triangle

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SAT Math › How to find the height of a triangle

Questions 1 - 4

1

An equilateral triangle has a side length of 4. What is the height of the triangle?

$\sqrt{12}$

$\sqrt{8}$

Explanation

Because the triangle is an equilateral triangle, you know that all sides have the same length, so all sides have the length of 4. Draw the triangle and label all sides as 4. Next, draw a point in the middle of one of the sides, and label each side as 2. Draw a line segment from the midpoint that you just created to the opposite angle of the triangle. That line segment is the height of the triangle. You can solve for it by using the Pythagorean theorem.

The Pythagorean theorem states that

In our scenario a = 2, c = 4, and you are solving for b. After plugging the numbers into the formula you get

and then

and then

and then $b = \sqrt{12}$

Therefore, the height of the triangle is $\sqrt{12}$

2

Trapequi1

In the figure above, AB = AD = AE = BD = BC = CD = DE = 1. What is the distance from A to C?

$\frac{1}{2}$

$\sqrt{3}$

$\sqrt{2}$

Explanation

Trapequi2

Trapequi3

Trapequi4

3

A triangles has sides of 5, 9, and $x$ . Which of the folowing CANNOT be a possible value of $x$ ?

$3$

$4$

$5$

$6$

$7$

Explanation

The sum of the lengths of the shortest sides of a triangle cannot be less than the third side.

3 + 5 = 8 < 9, so 3 can't be a value of x.

4

A triangle has a base of 5 cm and an area of 15 cm. What is the height of the triangle?

5 cm

3 cm

1.5 cm

6 cm

None of the above

Explanation

The area of a triangle is (1/2)*base*height. We know that the area = 15 cm, and the base is 5 cm, so:

15 = 1/2 * 5 * height

3 = 1/2 * height

6 = height

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