Answer:
[tex]ML = 58[/tex]
Step-by-step explanation:
Given
[tex]JK=3x+11, ML=10x-12, NP=45[/tex]
See attachment
Required
Length ML
First, calculate x using the following equivalent ratios
[tex]JK : NP = NP : ML[/tex]
Express as fraction
[tex]\frac{JK }{ NP} = \frac{NP }{ ML}[/tex]
Cross Multiply
[tex]JK * ML = NP * NP[/tex]
Substitute values:
[tex](3x +11) * (10x - 12) = 45 * 45[/tex]
Expand
[tex]30x^2 - 36x + 110x - 132 = 2025[/tex]
[tex]30x^2 +74x - 132 = 2025[/tex]
Collect like terms
[tex]30x^2 +74x - 132 - 2025=0[/tex]
[tex]30x^2 +74x -2157=0[/tex]
Using a calculator:
[tex]x \approx -10[/tex] and [tex]x \approx 7[/tex]
Given that:
[tex]ML=10x-12[/tex]
Substitute values for x
[tex]ML=10*-10-12 = -100 - 12 = -112[/tex]
[tex]ML=10*7-12 = 70 - 12 = 58[/tex]
ML cannot be negative; So:
[tex]ML = 58[/tex]
