A 34 cm long wire is bent in to a rectangle. The length of its diagonal is 13 cm. What
are the lengths of the sides of the rectangle
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Answer:
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A 34 cm long wire is bent in to a rectangle. The length of its diagonal is 13 cm. What are the lengths of the sides of the rectangle?
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ANSWER
Perimeter of the rectangle = Length of the wire 2(Length + Breadth) = 34
⇒ Length + Breadth = 17
Let the length of the rectangle be x cm.
⇒ Breadth of the rectangle = (17 - x) cm.
Using Pythagoras theorem,
x
2
+(17−x)
2
=13
2
x
2
+289−34x+x
2
=169
2x
2
−34x+120=0
x
2
−17x+60=0
Discriminant =b
2
−4ac=289−240=49
x=
2a
−b±
b
2
−4ac
=
2
17±
49
=
2
17±7
=12or5
When length, x = 12 cm, breadth, 17 - x = 5 cm
When length, x = 5 cm, breadth, 17 - x = 12 cm
Thus, the lengths of the sides of the rectangle are 12 cm and 5 cm.
Answer:
Perimeter of the rectangle = Length of the wire 2(Length + Breadth) = 34
⇒ Length + Breadth = 17
Let the length of the rectangle be x cm.
⇒ Breadth of the rectangle = (17 - x) cm.
Using Pythagoras theorem,
x 2+(17−x) 2
=13
2x 2+289−34x+x 2
=169
2x 2−34x+120
=0
x 2−17x+60
=0
Discriminant =b
2−4ac=289−240=49
x= 2a−b± b 2-4ac
= 217±49
= 217±7
=12or5
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