Triangle Area Comparison: Analyzing Three 5-12-13 Configurations

Which of the following triangles have the same areas?

101010121212555131313555888121212666666FFFEEEGGGCCCBBBAAAKKKJJJIIIDDDLLLHHH

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Step-by-step video solution

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00:00 Determine which of the following triangles have the same area
00:03 Apply the formula for calculating the triangle area
00:07 (height x by base) divided by 2
00:14 Substitute in the relevant values and solve to find the area
00:20 This is the area of triangle IJK
00:26 Apply the same method and calculate the areas of the other triangles
00:34 Substitute in the height and base of the triangle EFG
00:53 This is the area of the triangle EFG
01:05 Substitute in the height and base of the triangle ABC
01:16 Substitute in the height and base of triangle ABC
01:25 This is the area of triangle ABC
01:32 This is the solution

Step-by-step written solution

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1

Understand the problem

Which of the following triangles have the same areas?

101010121212555131313555888121212666666FFFEEEGGGCCCBBBAAAKKKJJJIIIDDDLLLHHH

2

Step-by-step solution

We calculate the area of triangle ABC:

12×52=602=30 \frac{12\times5}{2}=\frac{60}{2}=30

We calculate the area of triangle EFG:

6×102=602=30 \frac{6\times10}{2}=\frac{60}{2}=30

We calculate the area of triangle JIK:

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

Therefore, the triangles that have the same areas are ABC and EFG.

3

Final Answer

EFG and ABC

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?

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