Answer:
a) x = 12
b) NP = 3.56; NL = 4.44
Step-by-step 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
