The length of a rope is 4m2(3 − 2 + 7). A length of (12 + 5 − 7) is cut from this rope. What is the length of the remaining rope?
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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
Step-by-step explanation:
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