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Problem 449

The area of a certain triangle is 52 square feet and the height is 13 feet. What is the measure of the base of the triangle ?

Expert verified
The measure of the base of the triangle is 8 feet.
See the step by step solution

Step 1: Write down the formula for the area of a triangle

We'll use the formula for the area of a triangle: Area = (1/2) * base * height.

Step 2: Substitute the given information into the formula

We are given the area, which is 52 square feet, and the height, which is 13 feet. So, we can write the equation as: $$52 = (1/2) * base * 13$$.

Step 3: Solve for the base

To solve for the base, first we can simplify the equation by multiplying both sides by 2: $$2*52 = 2 * (1/2) * base * 13$$. This simplifies to $$104 = base * 13$$. Next, we will divide both sides of the equation by 13: $$\frac{104}{13} = \frac{base * 13}{13}$$.

Step 4: Calculate the measure of the base

Now we have that $$base = \frac{104}{13}$$. When we perform the division, we get that the base measures 8 feet.

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