The area of a right triangle is 40 square meters. If the length of its base is 10 meters, what is the height, in meters, of the triangle?
For geometry questions involving triangle area, immediately write the standard formula , then plug in the given values and solve algebraically for the missing variable. Be careful not to drop the factor, and simplify the numerical part (like ) before solving the resulting one-step equation; this keeps the arithmetic quick and reduces mistakes.
Hints
Recall the correct area formula
Think about the formula for the area of a triangle that uses base and height. It includes a factor of .
Substitute the given values
Plug in for the area and for the base into the triangle area formula, then write the equation in terms of .
Isolate the height
After simplifying the constants, you should get a simple one-step equation like . Solve this equation for by dividing.
Desmos Guide
Use Desmos to compute the height
In Desmos, type the expression (2*40)/10. The numerical result that Desmos shows is the value of the triangle's height in meters.
Step-by-step Explanation
Write the area formula for a triangle
For any triangle, the area is given by
where is the area, is the base, and is the height.
Substitute the known values
You are told:
- The area is square meters, so .
- The base is meters, so .
Substitute these into the formula:
Simplify the equation
First simplify :
So the equation becomes
Solve for the height
To isolate , divide both sides by :
So . The height of the triangle is 8 meters.