Answer:
40 cm
Step-by-step explanation:
The perimeter of a triangle is the sum of the three sides
The large triangle ACD will have a perimeter = AC + CD + AD
We have two right triangles ABC and BCD which make up ΔACD
Each right triangle has two sides provided
We start off by computing the lengths of the missing sides AC and BD
We will use the Pythagorean theorem to compute these lengths
Pythagorean theorem for right triangles
Square of the hypotenuse = sum of squares of other two sides
where the hypotenuse is the longest side
In triangle ABC, AC is the hypotenuse and AB = 12cm and BC = 8.4 cm are the other two sides
Therefore
[tex]AC^2 = AB^2 + BC^2\\\\AC^2 = 12^2 + 8.4^2\\\\AC^2 = 144+70.56\\\\AC^2 = 214.56\\AC = \sqrt{214.56} = 14.6479\\[/tex]
AC = 14.6 rounded to 1 decimal place
For triangle BCD we use a similar approach to finding the hypotenuse CD:
[tex]CD^2 = BC^{2} + BD^2\\\\CD^2 = 8.4^{2} + 4.1^{2}}\\\\CD^2 =70.56 + 16.81\\\\CD^2 = 87.37\\\\CD = \sqrt{87.37}\\\\CD= 9.3472[/tex]
CD = 9.3 rounded to 1 decimal place
Perimeter of ACD = AC + CD + AD
AD = 12 + 4.1 = 16.1 cm
Perimeter = 14.6 + 9.3 + 16.1 = 40 cm
