The perimeter of a triangle is the sum of its side lengths.
The perimeter of triangle ACD is 40 units
Start by calculating the values of x and y, using the following equivalent ratios
[tex]6 : 4 = x - 2 : x - 4[/tex]
[tex]6 : 10 = 6 + x - 2 : y[/tex]
So, we have:
[tex]6 : 4 = x - 2 : x - 4[/tex]
Express as fraction
[tex]\frac 64 = \frac{x-2}{x-4}[/tex]
Cross multiply
[tex]6x - 24 = 4x - 8[/tex]
Collect like terms
[tex]6x - 4x = 24 - 8[/tex]
[tex]2x = 16[/tex]
Divide both sides by 2
[tex]x = 8[/tex]
Also, we have:
[tex]6 : 10 = 6 + x - 2 : y[/tex]
Express as fraction
[tex]\frac 6{10} = \frac{6 + x -2}{y}[/tex]
Substitute 8 for x
[tex]\frac 6{10} = \frac{6 + 8 -2}{y}[/tex]
[tex]\frac 6{10} = \frac{12}{y}[/tex]
Cross multiply
[tex]6y = 120[/tex]
Divide both sides by 6
[tex]y = 20[/tex]
The perimeter of triangle ACD is then calculated as:
[tex]P =6 + x - 2 + y + x - 4 + 4[/tex]
Substitute values for x and y
[tex]P =6 + 8 - 2 + 20 + 8 - 4 + 4[/tex]
[tex]P =40[/tex]
Hence, the perimeter of triangle ACD is 40 units
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