Geometry Puzzle – Critical Thinking 16

Challenge:

Two sides of a triangle measure 10 and 5. Which of the following could be the area of the triangle?

A- 50

B- 35

C- 25

D- 2

E- 0.1

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We can find the maximum area of the triangle only when the given sides are placed at right angles. Why?
Let’s put 10 as the base and 5 as the height. Then, the area of the triangle is: \(\frac{10×5}{2}= 25\)
The angle less or more than 90 degrees between the sides reduce the area. (Draw it out for yourself). Hence, the area can be anything between 0 and 25.

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