中四數學方程題 ~_~

1. 長方形的周界是20cm。設長方形一邊的長度是(x+2)cm
(a)試以x表示該長方形的面積.
闊度 = (周界 -2 x長度)/2 = [20 – 2(x +2)]/2 =(20 – 2x -4)/2 = 8 – x
長方形的面積 = 長度 x闊度 = (x +2)(8 –x) = (-x^2+6x+16)

ANS: (-x^2+6x+16)
 

2.PQR是一個直角三角形，PQ=(x+4)cm、QR=(4x-1)cm和PR=(5x-3)cm。求x的值。
(5x-3)^2 = (x + 4)^2 + (4x-1)^2
25x^2 -30x + 9 =x^2 +8x + 16 +16x^2 – 8x + 1
25x^2 -30x + 9 = 17x^2 + 17
8x^2 -30x - 8 = 0
4x^2 -15x - 4 = 0
(4x + 1)(x – 4) = 0
x = 4, x = -1/4 (rejected because x is negative)
x = 4

ANS:4



3.一條長2.6m的梯子倚著一堵直立的牆壁。梯子底部與牆壁的距離比梯子頂部與地面的距離短1.4CM。梯子底部與牆壁的距離是多少?
梯子長2.6 m = 260 cm
Let x = 梯子底部與牆壁的距離
梯子頂部與地面的距離 = x + 1.4 cm
260^2 =x^2 + (x+1.4)^2
67600 = x^2 + x^2 +2.8x + 1.96
2x^2 + 2.8x + 1.96 - 67600 = 0
2x^2 + 2.8x - 67598.04 = 0
x^2 + 1.4x – 33799.02 = 0
x = [-1.4+-sq. root (1.96 + 4x1x33799.02)]/2 [Quadratic formula]
x = (-1.4 + 367.79/2)/2
x = 183.1 cm

梯子底部與牆壁的距離 = 183.1 cm = 1.83 m

Please check the input data.

ANS:1m