the perimeter of a rectangle is 30cm, the area of the rectangle is 50cm square.find the length of the rectangle
Answers
L*w =Area = 50
L*W=50 l= 50/w
2L + 2W = 30
2*50/w +2W= 30
100/W + 2W=30
100+2W^2 / w = 30
100+2W^2= 30 W
2W^2-30W+100=0
W^2-15W+50=0
W^2-10W-5W+50=0
W(W-10)-5(w-10)=0
(W-5)(W-10)=0
W= 5 Or 10
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Length of the rectangle will be 10 cm
Step-by-step explanation:
The area of rectangle = 50 cm square
L x B = 50 cm square
B = (50 cm square) / L ...................Eq. No. 1
The perimeter of the rectangle = 30 cm
2 X ( L + B ) = 30 cm
2 L + 2 B = 30 cm
2 L + 2 x (50 cm square/L) = 30 cm ...................From Eq. No. 1
2 L + (100 cm square / L) = 30 cm
( 2 L^2 + 100 cm square ) = L x 30 cm
2 L^2 + 100 - 30 L = 0
2 L^2 - 30 L + 100 = 0
2 (L ^2 - 15 L + 50 ) = 0
(L ^2 - 15 L + 50 ) = 0/2
(L ^2 - 15 L + 50 ) = 0
{L^2 - (5 + 10) L + 50} = 0
(L^2 - 5L - 10L + 50) = 0
L (L - 5) - 10 ( L - 5 ) = 0
(L - 5) ( L - 10 ) = 0
Now,
Taking ( L - 5 ) =0
L = 5 cm
Taking ( L - 10 ) =0
L = 10 cm
There are two values, to check the correct we have to do the following process:
On putting the first value of L in equation 1, we get:
B = (50 cm square) / 5
B = 10 cm square
Here we can see the value of Breadth > Length which is not possible practically.
So, the second value will be right i.e. L = 10 cm
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