Q.18 Mr. Ramkumar has a beautiful rectangular garden and a swimming pool (in the form of a cuboid) in his luxurious bungalow. The area of the garden is x2+2x-15. Q.18 (i) What are the dimensions of the garden ? *
(X-5) and (X+3)
(X+5) and (X+3)
(X+5) and (X-3)
(X-5) and (X-3)
This is a required question
Q. 18(ii) The water capacity of swimming pool up to the rim is x3-23x2+142x-120. What are the dimensions of the swimming pool ? *
(X-1),(X-10) and (X-12)
(X+1),(X+10) and (X+12)
(X-1),(X+10) and (X-12)
(X+1),(X-10) and (X+12)
This is a required question
Q.18 (iii) Find the perimeter of the garden : *
4x-4
2x-4
2x+4
4x+4
This is a required question
Q. 18(iv) The cost of painting the pool, if the cost of painting is Rs. 5/- per sq. unit *
25x2-405x+1370
25x2+405x+1370
25x2-405x-1370
none of these
dry
Answers
Nice question!! I think you have done hard work to write this question!!☺️
Answer:
Well, your answer are :-
18(i). (x+5) and (x-3)
(ii). (x-1), (x-12) and (x-10)
(iii). 2x+4
(iv). 25x2 - 405x + 1370
All you need to do is factorisation!
Hope this answer is helpful to you ☺️☺️☺️
Answer:
Step-by-step explanation:
(i) Given the area of the garden = x² + 2x - 15
We know that area of a rectangle = Length * Breadth
=> x² + 2x - 15 = Length * Breadth
=> x² + 5x - 3x - 15 = Length * Breadth (mid term splitting)
=> x(x + 5) - 3(x + 5) = Length * Breadth
=> (x + 5) (x -3) = Length * Breadth
On comparing, we get the dimensions of the garden to be (x+5) and (x-3)
Option C
(ii) Given the capacity of the swimming pool = x³-23x²+142x-120
We know that capacity = Volume
and Volume = Length * Breadth * Height
=> x³ - 23x² + 142x - 120 = Length * Breadth * Height
=> (x - 1) (x² -22x + 120) = Length * Breadth * Height (hit and trail)
=> (x - 1) (x² - 12x - 10x + 120) = Length * Breadth * Height
=> (x - 1) [x(x - 12)- 10(x - 12)] = Length * Breadth * Height
=> (x - 1) [(x - 12) (x - 10)] = Length * Breadth * Height
On comparing, we get the dimensions of the swimming pool to be (x - 1) (x - 12) and (x - 10)
Option A
(iii) We know that perimeter of a rectangle = 2(Length * Breadth)
= 2( x + 5 + x -3)
= 2( 2x + 2)
= 4x + 4
Option D
(iv) To find the cost of painting the pool, we need to find the surface area of the pool
We know that the surface area of the pool = 2(lh+bh+lb) - lb
where l = length of the pool
b= breadth of the pool
h = height of the pool
(x - 1) (x - 12) (x - 10)
Therefore, surface area = 2[(x-1)(x-12) + (x-12)(x-10)+ (x-1)(x-10) ] - (x-1)(x-10)
= 2[(x²-12x-x+12) + (x²-10x-12x+120) + (x²-10x-x+10)] - (x²-10x-x+10)
= 2[(x²-13x+12) + (x²-22x+120) + (x²-11x+10)] - (x²-11x+10)
= 2[3x²-46x+142] - (x²-11x+10)
= 6x²-92x+284 - x²+11x-10
= 5x²-81x+274 unit²
It is given the cost of painting per unit² is Rs. 5
We know that Cost = Area* Rate
=> Cost = (5x²-81x+274) * 5
= 25x² - 405x + 1370
Therefore, the cost of painting the swimming pool is
Rs. (25x² - 405x + 1370 )
Option A