Triangle Base Calculation: Finding BC When Area is 20 cm² and Height is 8

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

S=20S=20S=20888AAACCCBBBDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate BC
00:04 Examine the size of the sides and lines according to the given data
00:08 Apply the formula for calculating the area of a triangle
00:17 (height x base) divided by 2
00:22 Substitute in the relevant values and solve for BC
00:27 Multiply by the denominator to find BC
00:35 Isolate BC
01:03 This is the solution

Step-by-step written solution

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1

Understand the problem

The area of triangle ABC is 20 cm².

Its height (AD) is 8.

Calculate the length of the side BC.

S=20S=20S=20888AAACCCBBBDDD

2

Step-by-step solution

We can insert the given data into the formula in order to calculate the area of the triangle:

S=AD×BC2 S=\frac{AD\times BC}{2}

20=8×BC2 20=\frac{8\times BC}{2}

Cross multiplication:

40=8BC 40=8BC

Divide both sides by 8:

408=8BC8 \frac{40}{8}=\frac{8BC}{8}

BC=5 BC=5

3

Final Answer

5 cm

Practice Quiz

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

Can these angles form a triangle?

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