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What is the length of side AB if AC = 12 cm and BC = 16 cm? Enter your numeric answer. Do not include units.

1 Answer

sankarankalyanam

Jun 17, 2018

$¯ ¯¯¯¯ ¯ A C = 20$ $color(indigo)(bar(AC) = 20$

Explanation:

Given triangle is a right triangle.

Hence ${(A B)}^{2} = ({(A C)}^{2} + {(B C)}^{2}$ $(AB)^2 = ((AC)^2 + (BC)^2$

${(A C)}^{2} = (12^{2} + 16^{2})$ $(AC)^2 = (12^2 + 16^2)$

${(A C)}^{2} = 4^{2} \cdot (3^{2} + 4^{2}) = 4^{2} \cdot 5^{2}$ $(AC)^2 = 4^2 * (3^2 + 4^2) = 4^2 * 5^2$

$¯ ¯¯¯¯ ¯ A C = \sqrt{4^{2} \cdot 5^{2}} = 20$ $bar(AC) = sqrt(4^2 * 5^2) = 20$

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