A rectangular lawn measures 8m by 10m and is surrounded by a path of uniform width xm.
The total area of the path is 63m². Find x.
(8+2x*10+2x)-80=63
8(10+2x)+2x(10+2x)-80=63
80+16x+20x+4x²-80=63
4x²+36x=63
x²+9x=15.75
x²+9x+(4.5/2)²=15.75+(4.5/2)²
(x+4.5)²=36
x+4.5=+/-6
x=1.5 OR x=-1.5
x=1.5


L.H.S. = (x-10)(x-16)(8) = (8x-80)(x-16) = 8x(x-16)-80(x-16) = 8x²-128x-80x-1280 = 8x²-208x-1280 = R.H.S.


3c + 4l = 72
5c + 2l = 64

15c + 20l = 360
15c + 6l = 192

14l = 168
l = 12
5c + 2(12) = 64
5c + 24 = 64
5c = 40
c = 8

2a + c = 37.5
1a + 3c = 37.5

6a + 3c = 112.5
1a + 3c = 37.5

5a = 75
a = 15

30 + c = 37.5

c = 7.5



x² + y² = 25
x + y = 7
y = 7-x

x² + (7-x)² = 25
x² + 7(7-x)-x(7-x) = 25
x² + 49 - 7x - 7x + x² = 25
2x² -14x = -24
2x² - 14x + 24 = 0
(2x-6)(x-4) = 0
x = 3 OR x = 4

x = 3
(3) + y = 7
y = 4
(3, 4)

x = 4
(4) + y = 7
y = 3
(4, 3)





2x-3<7
2x<10
x<5

(2x-3)/3 < 7
2x-3 < 21
2x < 24
x < 12

5 < 7 - 2x < 13
4 < 6 - 2x < 12
-2 < -2x < 6
2 > 2x > -6
1 > x > -3

5 > 9 - 4x > 1
-4 > -4x > -8
4 < 4x < 8
2 < x < 1

x² - 6x + 5 > 0
(x - 5)(x + 1) > 0

3y² + 2y - 1 > 0
(3y - 1)(y + 1) > 0

y² > 4y + 5
y² - 4y - 5 > 0
(y - 5)(y - 1) > 0