The measures of the angles of △QRS are m∠Q=2x+4,m∠R=4x−12, and m∠S=3x+8.QR=y+9,RS=2y−7, and QS=3y−13. 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 QRSare m∠Q=2x+4, m∠R=4x−12 and m∠S=3x+8 and also we know that the sum of the measures of the angles of a triangle is 180.
Therefore, 2x+4+4x−12+3x+8=180
⇒9x=180
⇒x=20
Substitute the value of x in the measures of the angles that is:
m∠Q=2(20)+4=44
⇒m∠R=4(20)−12=68
⇒m∠S=3(20)+8=68
Therefore, △QRS is isosceles and QR=QS which means