in a rectangle it's perimeter is 50 cm. It's area is 100cm2. find the sides?
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Answered by
2
2(a+b)=50 cm[perimeter]
a+b=25
a=12.5+x
b=12.5-x
area=ab
100=(12.5+x)(12.5-x)
156.25-x²=100
x²=56.25
x=7.5
a=12.5+7.5=20 cm
b=12.5-7.5=5 cm
a+b=25
a=12.5+x
b=12.5-x
area=ab
100=(12.5+x)(12.5-x)
156.25-x²=100
x²=56.25
x=7.5
a=12.5+7.5=20 cm
b=12.5-7.5=5 cm
Answered by
1
Let the sides of the rectangle be a and b.
Perimeter = 2(a*b) = 50 cm
So, a+b = 25 cm.
Also, a*b = 100 cm^2
(a-b)^2 = (a+b)^2 - 4ab = 625 - 400 = 225
Thus, a-b = 15 cm.
Now, a+b+a-b = 2a = 25+15 = 40 cm
So, a = 20 cm and therefore, b = 5 cm.
Thus, the sides of the rectangle are 20 cm and 5 cm.
Perimeter = 2(a*b) = 50 cm
So, a+b = 25 cm.
Also, a*b = 100 cm^2
(a-b)^2 = (a+b)^2 - 4ab = 625 - 400 = 225
Thus, a-b = 15 cm.
Now, a+b+a-b = 2a = 25+15 = 40 cm
So, a = 20 cm and therefore, b = 5 cm.
Thus, the sides of the rectangle are 20 cm and 5 cm.
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