The perimeter of a square is increased by 25%. Find the percentage of increase in its area.
with correct explanation?
Answers
Answered by
0
Answer:
Let the side be 10 cm. Then the area will be
100
c
m
2
New side
=
125
%
o
f
10
=
12.5
c
m
;
A
r
e
a
=
(
12.5
)
2
=
156.25
Percentage increase in area
=
56.25
%
.
Alternatively: If x is the percentage increase in the side of a square, then increase in area is given by
x
+
x
+
x
×
x
100
=
2
x
+
x
2
100
=
25
+
25
+
25
×
25
100
=
56.25
%
Step-by-step explanation:
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Answered by
1
Answer:
56.25%
Step-by-step explanation:
Let each side of the square be a. Then, area = .a2
New side =125a/100=5a/4. New area = (5a/4)^2 = (25a^2/16)
Increase in area = 25a^2/16−a^2=9a^2/16
Increase% = [9a^2/16*1/a^2*100] % = 56.25%.
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