Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.
Step-by-step solution
Idea: Area = length × breadth. With the length fixed at 13, the area is 13 times the breadth, which is linear in the breadth.
- (i) Breadth 12 cm: area = 13 × 12 = 156 cm2.½ mark
- (ii) Breadth 10 cm: area = 13 × 10 = 130 cm2.½ mark
- (iii) Breadth 8 cm: area = 13 × 8 = 104 cm2.½ mark
- For breadth b cm: Area A = 13b cm2, a linear expression in b.1 mark
- The breadths 12, 10, 8 go down by 2 each time, and the areas 156, 130, 104 go down by 13 × 2 = 26 each time: a constant difference, so the areas form a linear pattern.½ mark
Check: 156 − 130 = 26 and 130 − 104 = 26 ✓ (constant difference).
Answer to write in the exam
Area = length × breadth
(i) 13 × 12 = 156 cm2
(ii) 13 × 10 = 130 cm2
(iii) 13 × 8 = 104 cm2
∴ Linear pattern: A = 13b (areas 156, 130, 104 decrease by 26 as breadth decreases by 2 cm)
Common mistakes that cost marks
- Using the perimeter 2(13 + b) instead of the area 13 × b.
- Writing the units of area as cm instead of cm2.
- Saying the areas go down by 2 each time (the change in breadth) instead of by 26.
How this can come in the exam
A rectangle has width 9 cm. When its length increases by 3 cm, its area increases by
- 3 cm2
- 12 cm2
- 27 cm2
- 9 cm2
Show answer
(C) 27 cm2
Area = 9l, so a 3 cm increase adds 9 × 3 = 27 cm2.
A rectangle has length 15 cm. Find its area for breadths 4 cm, 6 cm and 8 cm, and write the linear pattern.
Show answer
60, 90, 120 cm2 (1 mark). A = 15b; the area grows by 30 cm2 for every 2 cm of breadth (1 mark).Try one yourself
A rectangle has length 11 cm. Find the area when the breadth is 3, 5 and 7 cm, and write the pattern.
Show answer
33, 55, 77 cm2; A = 11b (up by 22 cm2 for each 2 cm).
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