Question

The sum of three segments measures 82 cm. The first is 4/9 of the second and the third exceeds the second by 16cm. Calculate the size of each segment.

Please help it’s for tmr

Answer 1

1. 12 cm
2. 27 cm
3. 43 cm

Explanation:

You have three segments totaling 82 cm, with the first being 4/9 of the second, and the third being 16 cm more than the second.

Equations

We can describe the relationship by the equations ...

a + b + c = 82

a = 4/9b

c = b +16

Solution

The equations give each segment in terms of the second one, so we can substitute those relations into the sum:

(4/9b) +b +(b +16) = 82

22/9b = 66

b = 66(9/22) = 27

a = (4/9)(27) = 12

c = 27 +16 = 43

The first segment is 12 cm; the second is 27 cm; and the third is 43 cm.

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Additional comment

We used an ad hoc solution based on the observation that segments 'a' and 'c' were defined in terms of 'b'. We could write the equations as a system of 3 linear equations in 3 unknowns, and solve using matrix methods:

• a +b +c = 82
• 9a -4b = 0
• -b +c = 16

The solution is shown in the attachment: a=12, b=27, c=43.