11.If the length of the rectangle is increased by 40% and its breadth is decreased by 40%, w
be the percentage change in its perimeter?
12. Which of the following triplets are Pythagorean?
Answers
Answer:
Let initial length = L ,initial breadth =B
therefore initial area= L*B
Final length =L+(40/100)L=1.4 L
Final breadth=B-(30/100)B=0.7 B
Final area=0.98 L*B
therefore there is decrease in area
decrease in area=0.02 L*B
% decrease in area=[math](0.02 L*B)/(L*B)*100=2[/math]%
Let's make it little more simple…
Suppose, the initial length is 100 and initial breadth is also 100. So, the initial area is 100x100= 10,000 .
Now when the length is increased by 40% then final length becomes 140 and when the breadth is increased by 30% ,then final breadth becomes 130. So, the final area will be 140x130= 18,200.Hence ,
Change in area = 18200- 10000= 8200
,% age change in area= (8200/10000)x100
= 82%.
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Let the LENGTH AND BREADTH of the rectangle be “l” and “b” respectively. So the area of the rectangle is= lb
On increasing the length by 40% and decreasing the breadth by 30% , the area of the NEW RECTANGLE
=(1.4)l X (0.7) B= 0.98 lb. Therefore the area of the newly formed rectangle will be = 2% less than the original one.
[0.98 lb- lb]/lb x 100= 0.02 x 100= 2%]
What will be the perimeter if length is increased by 40% and breadth is decreased by 40%?
Length of a rectangle is increased by 40% and the breadth is increased by 40%. Find the percent change in the area of the triangle?
If the breadth of a rectangle is increased by 40% and the length is reduced by 30%, then what will be the effect on the area?
I suppose an equal sided rectangle *(makes no difference, just easier to show) and denote the length of its sides by “a”
The area of the original rectangle is axa = a square Now do the changes. One side becomes (a+.40) the other (a-.30) The area of the new rectangle is
(a=.40)times (a-.30) After simplification it gives a square -.02. The new area is 2% less than the original
Such questions have been addressed hundreds of times in Quora. Please look up before posting ..
Change in area is given by :
A + B + AB/100
40 + (-30) + (40 x -30)/100
40 - 30 -12 = -2%
Or Area is reduced by 2%
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The original area is A = b × h
The new base and height are 40% more than b and h. That is 40% more than the original 100% of each.
So the new base B = 140% of b.
The new height H is 140% of h.
H = 1.4 × h and B = 1.4 ×b.
The new area is B×H = 1.4×b ×1.4 × h = 1.96 × bh.
Rectangle A has sides 100 cm x 10 cm. Its area = 100x10 = 1000 sq cm.
Rectangle B has sides 140 cm x 14 cm. Its area = 140x14 = 1960 sq cm.
Area of rectangle B - Area of rectangle A = 1960–1000 = 960 sq cm.
Percentage increase of area of B over A = 960*100/1000 = 96%.
Conclusion : By increasing the length and the breadth of a rectangle by 40% each, the area increases by 96%.