Question 169784
Hi, Hope I can help,
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If one side of a right triangle is 12 and its hypotenuse is 13, what is the length of the other side?
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The formula to find the Hypotenuse or sides is {{{ a^2+b^2=c^2 }}}, where "a" and "b" are the sides, and "c" is the hypotenuse
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We can replace "c" with the length of the hypotenuse (13), and we can replace "a" or "b" with "12" ( we will replace "a" )
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a = 12
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b = unknown
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c = 13
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{{{ a^2+b^2=c^2 }}} = {{{ (12)^2+b^2=(13)^2 }}} = {{{ 144+b^2=169 }}}
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We will now move "144" to the right side
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{{{ 144+b^2=169 }}} = {{{ 144-144+b^2=169-144 }}} = {{{ b^2=25 }}}, now we just take the square root of both sides
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{{{ b^2=25 }}} = {{{ sqrt(b^2)=sqrt(25) }}} = {{{ b = 5 }}} or {{{ b = -5 }}}
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Since lengths cannot be nagative, the length of the other side is "5"
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You can check by replacing "b" with "5" in the equation
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{{{ 144+b^2=169 }}} = {{{ 144+(5)^2=169 }}} = {{{ 144+25=169 }}} = {{{ 169 = 169 }}}, (True)
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The length of the other side is "5"
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{{{ 5 }}} is your answer
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Hope I helped, Levi