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2
Example 14: The area of a rectangle is x + 7x + 12. If its breadth is (x + 3), then find its length.
Solution: Let the length of the rectangle be ‘l’.
Breadth of the rectangle = (x + 3)

Area of the rectangle = length × breadth
2
⇒ x + 7x + 12 = l × (x + 3)
(
+
+
2
+
x + 7 x 12 x + 4 x 3 x 12 xx + 4 )+ 3 x ( + 4 )
2
l = = =
x 3 x 3 x + 3
+
+
(x + 3 )(x + 4 )
= = (x + 4)
x + 3
Thus, the length of the rectangle = (x + 4)
Practice Time 13C
1. Divide the following.
3
3 3 3
(a) 27x by 54x (b) 30m n by 6mn (c) 9x y z by xy z (d) 17ab c by –abc 2
2
3 4
2 3
2. Divide the following.
2
3
2
3
(a) 10a + 25a + 20a by 5a (b) –21x – 7x – 14x + 35 by –7x
3. Divide the following expressions as directed.
(a) 9x + 33 by 3x + 11 (b) 6x + 12x by x + 2
2
(c) 76ab(a + 5)(b – 4) by 38a(b – 4) (d) 3p(p + 1)(p + 2)(p + 3) by p(p + 2)
4. Factorise the expressions and divide them as directed.
2
2
2
(a) x – 5x + 6 by x – 3 (b) 2(9x – 16y ) by 3x + 4y
4
2
2
2
3
(c) 52y (25y – 49) by 26y (5y + 7) (d) (3x – 1875) by (3x – 75)
3
(e) 24x – 8x + 12x – 4 by 2x + 1
2
2
2
5. The area of a square is given by 4x + 12xy + 9y . Find the side of the square.
2
6. Our maths head of the depart-
3
2
1
ment decided to organise an Problem 1: (P ) Problem 2: (P ) Problem 3: (P )
2
2
‘Error Finding & Rectification’ 2x(2x – 5) = 4x – 25 5x + 3 = 5x x − 9 =+
x 3
competition to the basic in- 3 x 3
−
stinct of maths, concept more
firmly. All the three houses Blue House  7 
participate in this interesting Red House   7
competition and gave their Purple House  7 7
opinion as follows:
Based on the above information answer the following questions:
(a) Which problem is/are answered wrong by all the three houses?
(b) What is the correct expression of P ? (c) Which house replied P incorrect?
1
2
(d) Which house answered correct for P ?
3
Brain Sizzlers
The area of a square is 9t + 4 + 12t. Its length is increased by 3 m to make it a rectangle. Find
2
the length, breadth, and area of the rectangle.
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