One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 18 cm2. Find the lengths of all sides.
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Let x be the length of the longer side x>3, then the other side's length is x−3. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be
A1+18=A2
x(x−3)+18=(x+1)(x−2)
x²−3x+18=x²+x−2x−2
2x=202
x=10
So, the sides of the rectangle are 10 cm and (10−3)=7 cm long.
Let x be the length of the longer side x>3, then the other side's length is x−3. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be
A1+18=A2
x(x−3)+18=(x+1)(x−2)
x²−3x+18=x²+x−2x−2
2x=202
x=10
So, the sides of the rectangle are 10 cm and (10−3)=7 cm long.
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Let one side be x
Ao, another side = x + 3
Area = x(x +3)
New breadth = x +1
New length = x + 4
Area of new Rectangle = (x+1)(x+4)
Given that, (x+1)(x+4) - x(x+3) = 18
x^2 + 5x + 4 - x^2 - 3x = 18
2x + 4 = 18
x = 7 cm
Ao, length of remaining side = 7+3 = 10 cm
Ao, another side = x + 3
Area = x(x +3)
New breadth = x +1
New length = x + 4
Area of new Rectangle = (x+1)(x+4)
Given that, (x+1)(x+4) - x(x+3) = 18
x^2 + 5x + 4 - x^2 - 3x = 18
2x + 4 = 18
x = 7 cm
Ao, length of remaining side = 7+3 = 10 cm
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