Length exceeds breadth by 4cm.Perimeter is 50sq.cm.Find length and breadth.
Answers
Step-by-step explanation:
The length and breadth are 14 cm and 10 cm
Step-by-step explanation:
Given that the length of a rectangle exceeds its breadth by 4 cm .if length and breadth are each is increased by 3 cm , the area of the new rectangle is 81 square cm more than the given rectangle.
we have to find the length and breadth of rectangle.
Let the breadth of rectangle be x cm
∴ The length is x+4
Area=length \times breadth=x(x+4)=x^2+4xArea=length×breadth=x(x+4)=x
2
+4x
Now, length and breadth are each is increased by 3 cm
New length=(x+4)+3=x+7
New breadth=x+3
\text{New area=}(x+7)(x+3)=(x^2+10x+21) cm^2New area=(x+7)(x+3)=(x
2
+10x+21)cm
2
As the area of the new rectangle is 81 square cm more than the given rectangle.
⇒ x^2+10x+21=(x^2+4x)+81x
2
+10x+21=(x
2
+4x)+81
10x-4x=81-2110x−4x=81−21
6x=606x=60
x=\frac{60}{6}=10 cmx=
6
60
=10cm
∴ Length=x+4=10+4=14 cmLength=x+4=10+4=14cm
Breadth=x=10 cmBreadth=x=10cm
The length and breadth are 14 cm and 10 cm
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