Triangle Area Calculation: Express Area Using Height X and Base 6

Question

Look at the triangle ABC below.

BC = 6

AD = X

Express the area of the triangle using X.

00:09 Let's express the area of the triangle using X.

00:13 To do that, apply the formula for a triangle's area.

00:18 So, think of it as base, B.C., times height, H, divided by 2.

00:23 Here, we mark A.D. as our height, H.

00:31 Now, substitute the relevant values into the formula.

00:39 Go ahead and calculate, then solve for X.

00:44 And there you have it, that's your solution!

To express the area of triangle $\triangle ABC$ using $X$ , follow these steps:

Identify the base $BC = 6$ .
Identify the height as $AD = X$ .
Use the formula for the area of a triangle: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ .
Substitute the known values: $\text{Area} = \frac{1}{2} \times 6 \times X$ .
Simplify the expression: $\text{Area} = \frac{6X}{2}$ .
Further simplify: $\text{Area} = 3X$ .

Comparing this with the choices given, choices B ( $\frac{6X}{2}$ ) and C ( $3X$ ) are both valid representations of the area.

Therefore, the correct answer is that choices B and C are correct.

Answers B and C are correct.

Answers B and C are correct.