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Question

The measures of the angles of QRS are mQ=2x+4,mR=4x12, and mS=3x+8. QR=y+9,RS=2y7, and QS=3y13. The perimeter of QRS is:

A
11
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B
20
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C
44
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D
55
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E
68
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Solution

The correct option is A 55
It is given that the measures of the angles of triangle QRS are mQ=2x+4, mR=4x12 and mS=3x+8 and also we know that the sum of the measures of the angles of a triangle is 180.
Therefore, 2x+4+4x12+3x+8=180
9x=180
x=20
Substitute the value of x in the measures of the angles that is:
mQ=2(20)+4=44
mR=4(20)12=68
mS=3(20)+8=68
Therefore, QRS is isosceles and QR=QS which means
y+9=3y13
3yy=13+9
2y=22
y=11
Now consider the sum of the sides that is:
QR+RS+QS=y+9+2y7+3y13=6y11
Hence, the perimeter of triangle QRS is:
6y11=6(11)11=6611=55

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