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Two right-angled triangles are joined together to make a larger triangle ACD.
Calculate the perimeter of triangle ACD.
Give your answer correct to 1 decimal place. Pythagoras.

Two rightangled triangles are joined together to make a larger triangle ACD Calculate the perimeter of triangle ACD Give your answer correct to 1 decimal place class=

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Answer:

40.1

Step-by-step explanation:

the question asks to give your answer to one decimal place

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The perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.

The two right-angled triangles that were joined together are: triangle ACB and DCB.

Perimeter of ACD = AC + AB + BD + DC

Given,

CB = 8.4 cm

AB = 12 cm

BD = 4.1 cm

Find AC and DC using Pythagorean Theorem

Length of AC:

Based on Pythagorean Theorem, we have the following,

[tex]AC = \sqrt{AB^2 + CB^2}[/tex]

  • Substitute

[tex]AC = \sqrt{12^2 + 8.4^2}\\\\AC = \sqrt{214.56} \\\\AC = 14.65 $ cm[/tex]

Length of DC:

Based on Pythagorean Theorem, we have the following,

[tex]DC = \sqrt{BD^2 + CB^2}[/tex]

  • Substitute

[tex]DC = \sqrt{8.4^2 + 4.1^2}\\\\DC = \sqrt{87.4} \\\\DC = 9.35 $ cm[/tex]

Perimeter of triangle ACD = AC + AB + BD + DC

Perimeter of triangle ACD = 14.65 + 12 + 4.1 + 9.35

  • Perimeter of triangle ACD = 40.1 cm.

Therefore, the perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.

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