In Δ𝐴𝐵𝐶, 𝐴𝐵̅̅̅̅ 𝑖𝑠 𝑐𝑜𝑛𝑔𝑟𝑢𝑒𝑛𝑡 𝑡𝑜 𝐵𝐶̅̅̅̅. 𝑇ℎ𝑒 𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 𝑜𝑓 Δ𝐴𝐵𝐶 𝑖𝑠 82 𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑛𝑡𝑒𝑟𝑠. How many centimeters long is 𝐴𝐶̅̅̅̅?

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Answer 1 · 2018-03-29T00:44:52

$A C = 20 cm$ $AC = 20" cm"$

Because we are told that AB is congruent to BC, we know that the equation length of AB is, also, $4 x - 9$ $4x-9$ .

Add the lengths of the 3 sides together and set that equal to $82 cm$ $82" cm"$ :

$2 x + 4 x - 9 + 4 x - 9 = 82 cm$ $2x+4x-9+4x-9= 82" cm"$

Combine like terms:

$10 x - 18 = 82 cm$ $10x -18 = 82" cm"$

$10 x = 100 cm$ $10x = 100" cm"$

$x = 10 cm$ $x = 10" cm"$

The length of AC is:

$A C = 2 x$ $AC = 2x$

$A C = 2 (10 cm)$ $AC = 2(10" cm")$

$A C = 20 cm$ $AC = 20" cm"$