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I need help and I am struggling with this question. Please help

I need help and I am struggling with this question. Please help-example-1

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Answer:

a) x = 12

b) NP = 3.56; NL = 4.44

Explanation:

a)

Triangles NPQ and NLM are said to be similar. That means corresponding angles P and L have the same measure. This fact lets you solve for x.

angle L = angle P

3x +24 = 60 . . . . a 2-step linear equation

3x = 36 . . . . . . . step 1: subtract 24

x = 12 . . . . . . . . step 2: divide by the coefficient of x

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b)

Corresponding sides are proportional, so you have ...

NP/NL = NQ/NM

The length of PL is given, so you have an additional equation, ...

NP +NL = 8

This gives two equations in the two unknown values, NP and NL.

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Substituting the given values of NQ and NM, the first equation becomes ...

NP/NL = 3.2/4 = 0.8

Multiplying by NL, we get ...

NP = 0.8·NL

Substituting this into the equation for the sum gives ...

0.8·NL +NL = 8

1.8·NL = 8

NL = 8/1.8 = 40/9 = 4.4444...(repeating)

NP = 0.8·NL = 32/9 = 3.5555...(repeating)

Rounded to hundredths, the values are ...

NP ≈ 3.56, NL ≈ 4.44

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