The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq. Cm. Find the length of the rectangle. Select one:
a. 30 cm
b. 20 cm
c. 55 cm
d. 45 cm
Answers
Answered by
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Answer: Option C
Explanation:
Let breadth
=
x
cm
Then, length
=
2
x
cm
Area
=
x
×
2
x
=
2
x
2
sq.cm.
New length
=
(
2
x
−
5
)
cm
New breadth
=
(
x
+
5
)
cm
New area
=
(
2
x
−
5
)
(
x
+
5
)
sq.cm.
Given that, new area = initial area
+
75
sq.cm.
⇒
(
2
x
−
5
)
(
x
+
5
)
=
2
x
2
+
75
⇒
2
x
2
+
10
x
−
5
x
−
25
=
2
x
2
+
75
⇒
5
x
−
25
=
75
⇒
5
x
=
75
+
25
=
100
⇒
x
=
100
5
=
20
cm
Length
=
2
x
=
2
×
20
=
40
cm
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