Right Triangle Solution: Finding Side Length BC with Area 36

Q: Why do we use 1/2 in the triangle area formula?

A right triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space, so we multiply by 1/2.

Q: Which sides should I use as base and height?

In a right triangle, use the two sides that form the 90-degree angle (the perpendicular sides). The hypotenuse is never used in the area calculation.

Q: What if I get confused about which formula to use?

For right triangles, always use $ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $. The base and height are the two sides that meet at the right angle.

Q: Can I check my answer a different way?

Yes! Calculate the area using your answer: $ \frac{1}{2} \times 12 \times 6 = 36 $. If you get the original area, your answer is correct!

Triangle Area with Known Side Length

ABC is a right triangle with an area of 36.

Calculate the length of side BC.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the value of BC

00:02 Apply the formula for calculating the triangle's area

00:06 (height(AB) x base(BC)) divided by 2

00:10 Substitute in the relevant values and calculate to find BC

00:20 Divide 12 by 2 to obtain 6

00:23 Isolate BC

00:30 That's the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABC is a right triangle with an area of 36.

Calculate the length of side BC.

Step-by-step solution

To solve for the length of side $BC$ in the right triangle $\triangle ABC$ , we start with the formula for the area of a right triangle:

$\text{Area} = \frac{1}{2} \times AB \times BC$

We know the area of the triangle is 36, and the length of side $AB$ is 12. We'll substitute these values into the formula:

$36 = \frac{1}{2} \times 12 \times BC$

To isolate $BC$ , first multiply both sides of the equation by 2 to eliminate the fraction:

$72 = 12 \times BC$

Now, solve for $BC$ by dividing both sides of the equation by 12:

$BC = \frac{72}{12}$

Upon simplifying, we find:

$BC = 6$

Thus, the length of side $BC$ is $\boxed{6}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Area Formula: Right triangle area equals half times base times height
Technique: Substitute known values: 36 = (1/2) × 12 × BC
Check: Verify calculation: (1/2) × 12 × 6 = 36 ✓

Common Mistakes

Avoid these frequent errors

Forgetting the 1/2 factor in area formula
Don't calculate area as just base × height = 12 × BC! This gives double the actual area and wrong answers. Always remember the area formula for right triangles includes the 1/2 factor.

Practice Quiz

Test your knowledge with interactive questions

Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

FAQ

Everything you need to know about this question

Why do we use 1/2 in the triangle area formula?

A right triangle is half of a rectangle! If you draw a rectangle with the same base and height, the triangle takes up exactly half the space, so we multiply by 1/2.

Which sides should I use as base and height?

In a right triangle, use the two sides that form the 90-degree angle (the perpendicular sides). The hypotenuse is never used in the area calculation.

What if I get confused about which formula to use?

For right triangles, always use $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$ . The base and height are the two sides that meet at the right angle.

How do I solve when the area equation has fractions?

Multiply both sides by 2 first to eliminate the fraction, then solve normally. For example: $36 = \frac{1}{2} \times 12 \times BC$ becomes $72 = 12 \times BC$ .

Can I check my answer a different way?

Yes! Calculate the area using your answer: $\frac{1}{2} \times 12 \times 6 = 36$ . If you get the original area, your answer is correct!

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