SECTION - II
Case study based questions are compulsory. Attempt any four sub parts of each questions. Each subpart carries
17. A hall has dimensions 32 m by 20 m. Part of the floor of the hall is covered with ceramic tiles,
as shown by the shaded rectangle in the figure. Part of the floor not covered by the tiles has a
uniform width of'x'm.
On the basis of the above information, answer the following questions :
(i) The expression, in terms of x. for the breadth of the floor covered by the tiles is:
(a) 32 - 2x
(b) 20 -- 2x
(c) 32-
(d) 20 - X
(ii) The expression, in terms of x. for the length of the floor covered by the tiles is:
(a) 20 - 2
(b) 20 -
(c) 32 -
(d) 32 - 2x
(u)Given that the floor area covered by the tiles is 448 sq cm, what equation, in terms of x. is formulated?
(a) - 26x + 48=0
(b) 2r- - 13x + 24 = 0
(c)-2x + 12 - 0
(d) 3r - 6x + 16 = 0
iy) What is the width of the floor not covered by the tiles?
fa) 1.5 m
(b) 2 m
(c) 25 m
(d) 3 m
(w) What is the cost of tiling at the rate of 7 28 per sq m?
(a) 12.544
(b) 13,664
(c) 211.648
(d) 8064
Answers
Given : A hall has dimensions 32 m by 20 m.
Part of the floor of the hall is covered with ceramic tiles,
Part of the floor not covered by the tiles has a uniform width of 'x' m.
To Find : i) The expression, in terms of x. for the breadth of the floor covered by the tiles is:
(ii) The expression, in terms of x. for the length of the floor covered by the tiles is:
Given that the floor area covered by the tiles is 448 sq cm, what equation, in terms of x. is formulated?
What is the width of the floor not covered by the tiles?
What is the cost of tiling at the rate of 7 28 per sq m?
Solution:
i) The expression, in terms of x. for the breadth of the floor covered by the tiles is: = 20 - 2x
(ii) The expression, in terms of x. for the length of the floor covered by the tiles is: = 32 - 2x
Area covered by tiles = (32 - 2x)(20 - 2x) = 448
=> (16 - x)(10 - x) = 112
=> 160 + x² - 26x = 112
=> x² - 26x + 48 = 0
x² - 24x - 2x + 48 = 0
=> (x - 24)(x - 2) = 0
=> x= 24 or x = 2
x = 24 not possible
Hence x = 2
width of the floor not covered by the tiles = 2 m
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