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[/tex] ≈ [tex]-10[/tex] and [tex]x[/tex] ≈ [tex]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]
