Examples with solutions for Area of a Triangle: Ascertaining whether or not there are errors in the data

Exercise #1

Given the triangle ABC

AD=6 CE=3 CB=5

What should be the length of AB so that the area of a triangle ABC is compatible with the rest of the data in the drawing?

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Video Solution

Step-by-Step Solution

Given that AD is perpendicular to CB

We can establish that AD is the height of the triangle ADB

Hence the formula for the area of triangle ABC=

AD×CB2 \frac{AD\times CB}{2}

We insert the existing data into the formula:

6×52=302=15 \frac{6\times5}{2}=\frac{30}{2}=15

Due to the fact that CE is also a height, we can calculate the area of triangle ABC as follows:

CE×AB2 \frac{CE\times AB}{2}

Since we found the area of triangle ABC, we will insert the data into the formula:

15=3×AB2 15=\frac{3\times AB}{2}

We then multiply across:

30=3AB 30=3AB

Lastly we divide both sides by 3:

303=3AB3 \frac{30}{3}=\frac{3AB}{3}

AB=10 AB=10

Answer

10 cm

Exercise #2

In which part of the drawing was an error made?

so that the area of the triangle is 24 cm²? Which data should be in place of the error?

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Video Solution

Answer

EG=4.8

Exercise #3

In triangle ABC given in cm:

AC=10 BD=12 AB=20 EC=5

Which of the data must be changed so that the area of a triangle ABC is 60 cm²?

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Video Solution

Answer

Answer B or answer C is correct