Question

Find ML, JK=3x+11, ML=10x-12, NP=45

Answer 1

Answer:

$ML = 58$

Step-by-step explanation:

Given

$JK=3x+11, ML=10x-12, NP=45$

See attachment

Required

Length ML

First, calculate x using the following equivalent ratios

$JK : NP = NP : ML$

Express as fraction

$\frac{JK }{ NP} = \frac{NP }{ ML}$

Cross Multiply

$JK * ML = NP * NP$

Substitute values:

$(3x +11) * (10x - 12) = 45 * 45$

Expand

$30x^2 - 36x + 110x - 132 = 2025$

$30x^2 +74x - 132 = 2025$

Collect like terms

$30x^2 +74x - 132 - 2025=0$

$30x^2 +74x -2157=0$

Using a calculator:

$x \approx -10$ and $x \approx 7$

Given that:

$ML=10x-12$

Substitute values for x

$ML=10*-10-12 = -100 - 12 = -112$

$ML=10*7-12 = 70 - 12 = 58$

ML cannot be negative; So:

$ML = 58$