MAths trouble... plz help >v< (need people who good at math)

[匿名]

2008-08-09 9:38 pm

1. The perimeter and are of a rectangle are 14 cm and 10cm2 respectively. Find its dimensions.

2. A rectangular flowerbed of length 30m and width 20m is surrounded by a parthway of uniform width. If the area of the pathway is 216m2 , find thd its width.

3. If point L( -2, a ) is on the graph of the linear equation y = 4x plus 3, find the value of a.

回答 (1)

Uncle Michael

2008-08-09 10:53 pm

✔ 最佳答案

1)
Let a cm x b cm be its dimensions.

Consider the perimeter:
2(a+b) = 14
a+b = 7
b = 7-a ..... (1)

Consider the area:
ab = 10 ..... (2)

Substitute (1) into (2):
a(7-a) = 10
a2-7a+10 = 0
(a-2)(a-5) = 0
a = 2 oorr a = 5

Substitute the value of a into (1)
b = 5 oorr b = 2

Hence, its dimensions are 2 cm x 5 cm.

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2)
Let y m be the width of the pathway.

Consider the total area in m:
(30+2y)(20+2y) = 30x20 + 216
600 + 100y + 4y2 = 600 + 216
4y2 + 100y - 216=0
y2 + 25y - 54 = 0
(y-2)(y+27) = 0
y = 2 oorr y = -27(rejected)

Hence, the width of the pathway is 2 m.

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3)
(-2, a) lies on the line y = 4x + 3.

(-2) = 4a + 3
4a = -5
a = -5/4
=

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