A triangle has a base of length 14 centimeters and an area of 42 square centimeters. What … — GRE General Test

A triangle has a base of length $14$ centimeters and an area of $42$ square centimeters. What is the height, in centimeters, of the triangle perpendicular to this base?

Answer: 6 cm

Answer

The height of the triangle perpendicular to the base is 6 centimeters.

The area of a triangle is given by

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

. Substituting

42

for the area and

14

for the base yields

42 = \frac{1}{2} \times 14 \times h

, which simplifies to

42 = 7h

. Dividing

42

7

gives

h = 6

Step-by-Step Solution

Write down the triangle area formula.

\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}

The area and base are known values, and the goal is to solve for the perpendicular height.

Substitute the given values into the formula.

42 = \frac{1}{2} \times 14 \times \text{height}

Plugging in

\text{Area} = 42

and

\text{base} = 14

creates a single-variable algebraic equation.

Solve for the height.

42 = 7 \times \text{height} \implies \text{height} = 6

Simplifying

\frac{1}{2} \times 14

7

and dividing both sides by

7

yields the height.

Key Concept

The area of a triangle is calculated using the formula Area = (1/2) * base * height.

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