maths

Let a cm be the length of the rectangle, and b cm be the width.

2(a + b) = 52 …… (1)
(a + 4)(b/2) = ab - 60 …… (2)

(1):a + b = 26
b = 26 - a …… (3)

Sub. (3) into (2):
(a + 4)(26 - a)/2 = a(26 - a) - 60
(a + 4)(26 - a) = 2a(26 - a) - 120
104 + 22a - a² = 52a - 2a² - 120
a² - 30a + 224 = 0
(a - 16)(a - 14) = 0
a = 16 or a = 14

(3):
When a = 16, b = 10
When a = 14, b = 12

The dimension of the rectangle is 16 cm x 10 cm or 14 cm x 12 cm.

2010-07-11 01:13:26 補充：
y= -2x² + 7x + 4
y = -2[x² - (7/2)x] + 4
y = -2[x² - (7/2)x + (7/4)²] + 2(7/4)² + 4
y = (81/8) - 2[x - (7/4)]²

-2[x + (7/4)]² ≤ 0
When x = 7/4
max. of y = 81/8

PLS also answer the following question. THX.

The figure shows the graph of y= -2x^2+7x+4. It passes through the points (3,7) and (0,4).

Find the maximum point of the graph.

PLS answer!