Chapter 1 Quadratic Equations In One Unknown Worksheet With Answers Page 28
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34Number and Algebra
Number and Algebra
4.
The length of a rectangular garden is 4 m longer than its width. If the numerical value of the
product of the length and the width is greater than half the numerical value of the perimeter of the
garden by 44. Find the length and the width of the garden.
Solution
Let x m be the width of the garden,
then ( x + 4) m is the length of the garden.
+
+
2
(
x
(
x
4
))
∴
+
=
+
x x
(
4
)
44
2
+
=
+
2
x
4
x
2
x
48
+
−
=
2
x
2
x
48
0
−
+
=
(
x
6
)(
x
8
)
0
x = 6 or x = −8 (rejected)
∴ The width and the length of the garden are 6 m and (6 + 4) m = 10 m.
5.
A copper wire is cut into three portions. The three portions are bent to form squares A, B and C.
The lengths of sides of squares B and C are longer than that of square A by 6 cm and 12 cm
2
respectively. If twice the area of square A is smaller than the area of square B by 8 cm
, find the
length of the copper wire.
Solution
Let x cm be the length of a side of square A , then ( x + 6) cm and ( x + 12) cm are the lengths of
sides of squares B and C respectively.
= ( x + 6)
− 8
2
2
2 x
= x
+ 12 x + 28
2
2
2 x
− 12 x − 28 = 0
2
x
( x − 14)( x + 2) = 0
x = 14 or x = −2 (rejected)
∴
The length of the copper wire
= 4[ x + ( x + 6) + ( x + 12)] cm
= 4[14 + (14 + 6) + (14 + 12)] cm
= 240 cm
28
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education