The area of a right triangle is 48 square centimeters, and its base measures 12 centimeters. What is the height, in centimeters, of the triangle?
For area and volume questions, start by writing the correct formula (here, ), then plug in the given numbers before doing any algebra. Simplify the constants carefully—especially fractions like —to avoid small arithmetic mistakes, and then solve the resulting simple equation in one or two steps. Always check whether you should be multiplying or dividing in the final step, since many wrong answers come from that last operation.
Hints
Use the triangle area formula
What is the formula that relates a triangle’s area, its base, and its height?
Plug in what you know
In the area formula, substitute 48 for the area and 12 for the base, then simplify the constants.
Solve the simple equation
After simplifying, you should get an equation of the form . What do you get when you divide 48 by that constant ?
Desmos Guide
Compute the height directly
In Desmos, type the expression 48 / (0.5 * 12) and press Enter. The value that Desmos returns is the height of the triangle in centimeters.
Step-by-step Explanation
Recall the area formula for a triangle
The area of any triangle (including a right triangle) with base and height is given by
Here, the base is 12 centimeters, the height is unknown, and the area is 48 square centimeters.
Substitute the known values and simplify
Substitute and into the formula:
Now simplify :
So the equation becomes
Solve for the height
To find , divide both sides of the equation by 6:
So . The height of the triangle is 8 centimeters.