A rope of leangth 40cm is cut into pieces is cut intopieces andtwo sqares aremade on the floor with then the sum of the In close is 58cm2.a) if the leangth of theone piece is taken as x what is the leangth of the other piece
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Answer:
Length of the rope =40cm let length of the piece =x
a. Length of the other piece =40−x
b. Length of the sides of the square
=
4
x
and
4
40−x
c. The algebraic form, Given, sum of the area 58cm
2
.
ie., a
2
+a
2
=58cm
2
.
⇒(
4
x
)
2
+(
4
40−x
)
2
=58
⇒
16
x
2
+
16
1600−80x+x
2
=58
⇒2x
2
−80x+1600=58×16
1x
2
−80x+1600=928
dividing through out by 2,
ie., x
2
−40x+800=464.
⇒x
2
−40x+800−464=0
⇒x
2
−40x+800−464=0
⇒x
2
−40x+336=0
Length of each piece,
x
2
−40×336=0 (factorize)
⇒(x−28)(x−12)=0
⇒x−28=0 or x−12=0
x=28 or x=12
The length of each pieces =28m or 12m.
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