The length of the hypotenuse in a right triangle is 20 centimeters. If the length of one leg is 16 centimeters, what is the length of the other leg?

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Answer 1 · 2018-04-24T02:57:04

$12 cm$ $"12 cm"$

From $Pythagoras Theorem$ $"Pythagoras Theorem"$

$h^{2} = a^{2} + b^{2}$ $"h"^2 = "a"^2 + "b"^2$

where

${(20 cm)}^{2} = {(16 cm)}^{2} + b^{2}$ $("20 cm")^2 = ("16 cm")^2 + "b"^2$

$b^{2} = {(20 cm)}^{2} - {(16 cm)}^{2}$ $"b"^2 = ("20 cm")^2 - ("16 cm")^2$

$b = \sqrt{{(20 cm)}^{2} - {(16 cm)}^{2}}$ $"b" = sqrt(("20 cm")^2 - ("16 cm")^2)$

$b = \sqrt{{400 cm}^{2} - {256 cm}^{2}}$ $"b" = sqrt("400 cm"^2 - "256 cm"^2)$

$b = \sqrt{{144 cm}^{2}}$ $"b" = sqrt("144 cm"^2)$

$b = 12 cm$ $"b = 12 cm"$