In Δ𝐴𝐡𝐢, 𝐴𝐡̅̅̅̅ 𝑖𝑠 π‘π‘œπ‘›π‘”π‘Ÿπ‘’π‘’π‘›π‘‘ π‘‘π‘œ 𝐡𝐢̅̅̅̅. π‘‡β„Žπ‘’ π‘π‘’π‘Ÿπ‘–π‘šπ‘’π‘‘π‘’π‘Ÿ π‘œπ‘“ Δ𝐴𝐡𝐢 𝑖𝑠 82 π‘π‘’π‘›π‘‘π‘–π‘šπ‘’π‘›π‘‘π‘’π‘Ÿπ‘ . How many centimeters long is 𝐴𝐢̅̅̅̅?

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1 Answer
Douglas K.
Mar 29, 2018

#AC = 20" cm"#

Explanation:

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

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

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

Combine like terms:

#10x -18 = 82" cm"#

#10x = 100" cm"#

#x = 10" cm"#

The length of AC is:

#AC = 2x#

#AC = 2(10" cm")#

#AC = 20" cm"#

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