Question

The area of a triangle is 40.0 cm^2. What is the height?

A) 10 cm
B) 8 cm
C) 5 cm
D) 20 cm

Answer 1

To find the height of a triangle with a given area, we can use the formula for the area of a triangle. By rearranging the formula, we can calculate the height by dividing the area by half of the base. Substituting the given values into the formula, we find that the height is 10 cm. Hence, option B) 8 cm is the correct answer.

Step-by-step explanation:

To find the height of a triangle when the area is given, we use the formula:

Area = 1/2 × base × height

In this case, the area is given as 40.0 cm^2. Let's substitute the values into the formula:

40.0 cm^2 = 1/2 × base × height

Since we only need to find the height, we can rearrange the formula:

Height = Area / (1/2 × base)

Substituting the given values:

Height = 40.0 cm^2 / (1/2 × base)

Now, we just need to calculate the height using the given options and select the correct one.

Option A) 10 cm: Height = 40.0 cm^2 / (1/2 × base) = 40.0 cm^2 / (1/2 × 10 cm) = 40.0 cm^2 / 5 cm = 8 cm

Option B) 8 cm: Height = 40.0 cm^2 / (1/2 × base) = 40.0 cm^2 / (1/2 × 8 cm) = 40.0 cm^2 / 4 cm = 10 cm

Option C) 5 cm: Height = 40.0 cm^2 / (1/2 × base) = 40.0 cm^2 / (1/2 × 5 cm) = 40.0 cm^2 / 2.5 cm = 16 cm

Option D) 20 cm: Height = 40.0 cm^2 / (1/2 × base) = 40.0 cm^2 / (1/2 × 20 cm) = 40.0 cm^2 / 10 cm = 4 cm

Based on these calculations, the correct height of the triangle is 10 cm.

Answer 2

Without the length of the base of the triangle, the height cannot be determined from the given area, as multiple combinations of base and height can result in the same area.

Step-by-step explanation:

To solve for the height of the triangle given its area, we use the area formula of a triangle, which is area = 1/2 × base × height. However, the base is not provided in the problem statement. This makes it impossible to determine the height as there are infinitely many combinations of base and height that can give the same area. Thus, without additional information, particularly the length of the base of the triangle, the height cannot be determined.