Find X: Triangle with Area 15 and Base 3

Question

Since the area of the triangle is equal to 15.

Find X.

00:11 Let's find the height X of this triangle.

00:15 We'll use the triangle area formula, which you might remember from class.

00:20 The area equals base times height, divided by 2. Here, the base is BC, and the height is AE.

00:28 Now, let's plug in our values and solve for the height X.

00:32 To make our calculation easier, let's multiply both sides by 2 to get rid of fractions.

00:39 Next, we'll isolate X by itself to find our answer.

00:45 And there we have it! We've found the height X of our triangle.

To solve for $x$ , let's apply the standard formula for the area of a triangle:

The area formula is:

$A = \frac{1}{2} \times b \times h$

Substituting the given values into the equation, we have:

$15 = \frac{1}{2} \times 3 \times x$

Now, simplify and solve for $x$ :

$15 = \frac{3}{2} \times x$

Multiply both sides by $\frac{2}{3}$ to isolate $x$ :

$x = 15 \times \frac{2}{3}$

Calculating, we obtain:

$x = \frac{30}{3} = 10$

Thus, the height $x$ of the triangle is $x = 10$ .

Therefore, the solution to the problem is $x = 10$ .