Area of a Triangle: Ascertaining whether or not there are errors in the data

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

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?

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=

$\frac{AD\times CB}{2}$

We insert the existing data into the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

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

$\frac{CE\times AB}{2}$

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

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

We then multiply across:

$30=3AB$

Lastly we divide both sides by 3:

$\frac{30}{3}=\frac{3AB}{3}$

$AB=10$

10 cm

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?

Answer B or answer C is correct

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?

EG=4.8