The Me
Favorite Answer
11. The length is L, the width is W
2L+2W=44
LW=40
W=40/L
2L+2(40/L)=44
2L+80/L=44
2L^2+80=44L
L^2-22L+40=0
(L-2)(L-20)=0
L=2 or L=20
W=2 or W=20
The rectangle is 2 by 20
12.The length is L, the width is W
2L+2W=38
LW=84
W=84/L
2L+2(84/L)=38
L+84/L=19
L^2+84=19L
L^2-19L+84=0
(L-12)(L-7)=0
The rectangle is 12 by 7
13. (x+2)(x+5)=130
x^2+7x+10=130
x^2+7x-120=0
(x+15)(x-7)=0
x=-15 or x=7
The side of the square is 7
14. L=2W
(L-3)(w+2)=30
(2w-3)(w+2)=30
2w^2+w-6=30
2w^2+w-36=0
(2w+9)(w-4)=0
W=-9/2 or W=4
W=4, L=8
The rectangle is 8 by 4
15. L=3W
(L+2)(W-1)=68
(3W+2)(W-1)=68
3w^2-W-2=68
3W^2-W-70=0
(3W+14)(W-5)=0
w=-14/3 or w=5
The rectangle is 5 by 15
Philip
B.11. Rectangle has length L and width W. L+W = (1/2)perimeter =(1/2)44 = 22. Therefore W = 22 - L. Now area
= 40. Therefore LW = 40 so L(22- L) = 40, ie., L^2 - 22L = - 40, ie., (L-11)^2 = 121-40 = 81 = 9^2, L = 11(+/-)9.
Clearly, L = 20, W = 2. [linear units = cm, area units = cm^2].
B.12. L+W =(1/2)38 =19. Therefore W =19 - L. Now area = 84, ie.,LW = 84, ie., L(19-L) =84, ie.,L^2 -19L+84=0,
ie., (L-7)(L-12) = 0, ie., L = 12, W = 7 [units: linear m, area m^2, m = meter.]
B.13. Dimensions of resulting rectangle are L by W, where L = x+5 and W = x+2. Then rectangle area, LW, =
(x+5)(x+2) =130, ie., x^2 + 7x - 120 =0, ie.,(x-8)(x+15) =0, ie., x =8 {since x > 0} Square side length = 8 cm.