Question 240431: if a rectangle has an area of 117cm2 and a perimeter of 44cm what is it's length and breadth Found 2 solutions by stanbon, checkley77:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! if a rectangle has an area of 117cm2 and a perimeter of 44cm what is it's length and breadth
------------------------
width = x
length = y
-----------------
Area = xy = 117 cm^2
Perim = 2(x+y) = 44 cm
----------------------------
x+y = 22
---------------------
Solve for y:
y = 22-x
-------------------
Substitute into xy = 117 and solve for "x":
x(22-x) = 117
-x^2 + 22x - 117 = 0
x^2 - 22x + 117 = 0
--------------------
Quadratic formula:
x = [22 +- sqrt(22^2 - 4*117)]/2
x = [22 +- sqrt(16)]/2
Positive solution:
x = [11 + 2] = 13 (width)
-------------------------
Since x+y = 22, y = 22-13 = 9 (length)
============================================
Cheers,
Stan H.
You can put this solution on YOUR website! LW=117
L=117/W
2L+2W=44
2(117/W)+2W=44
234/W+2W=44
(234+2W^2/W=44
(234+2W^2)/W=44
2W^2+234=44W
2W^2-44W+234=0
2(W^2-22W+117)=0
2(W-13)(W-9)=0
W-13=0
W=13 ANS.
L*13=117
L=117/13
L=9 ANS
2*9+2*13=44
18+26=44
44=44
PROOF:
(