Question

Find ml if jk is 3x+11 and np is 45 and ml is 10x-12

trapezoid
it goes J to K
N to P
M to L
2 halvs
Kp is congruent to PL and Jn is congruent to NM

Answer 1

`ML=58`

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

`(JK)/(NP)=(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` ≈
`-10` and
`x` ≈
`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`