Case Study 2:- While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide.
Based on the above information, answer the following questions:
(i) Write an algebraic equation depicting the above information. 1
(ii) Write the corresponding quadratic equation in standard form. 1
(iii) What should be the new dimensions of the enlarged photo ? 2
OR
Can any rational value of x make the new area equal to 220 cm² ?
Solution:- Length of original photo = 18 cm
Breadth of the photo = 12 cm
Area of the photo = l×b = 18×12
= 216 cm²
Increase length = x cm
Increase breadth = x cm
New length = 18 + x
New bredth = 12 + x
(i) According to the question
(18 + x)(12 + x) = 2×216 = 432
(ii) (18 + x)(12 + x) = 2×216 = 432
216 + 18 x + 12 x + x² = 432
⇒ x² + 30 x – 432 + 216 = 0
⇒ x² + 30 x – 216 = 0
Now standard form of the quardratic equation
x² + 30 x – 216 = 0
(iii) x² + 30 x – 216 = 0
⇒ x² + 36 x – 6x – 216 = 0
⇒ x(x + 30) – 6(x + 30) = 0
⇒ (x + 30)(x – 6) = 0
Now, x = 6, -30
New length of the photo = 18 + 6 = 24 cm
New bredth of the photo = 12 + 6 = 18 cm
OR
From the equation
(18 + x)(12 + x) = 220
⇒ 216 + 12 x + 18 x + x² = 220
⇒ x² + 30x + 220 – 216 = 0
⇒ x² + 30x + 4 = 0
a = 1, b = 30, c = 4
Now,
b² – 4ac = (30)² – 4×1×4
= 900 – 16 = 884 > 0
There is no rational value of x for which the area of photo will be 220 cm²
Case Study 1:- the discus throw is an event in which an athlete attempts to throw a discus. The sthlete spins anti-clockwise around one and half times through a circle, then releases the throw. When released, the discus travels along tangent to the circular spin orbit.
In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre and ∠ABO = 30°. PQ is parallel to OA.
Based on above information :
(a) Find the length of AB. 1
(b) Find the length of OB. 1
(c) Find the length of AP. 2
OR
Find the length of PQ. 2
Solution:- See full solution
Case Study 3:- India meteorological department observes seasonal and annual rainfall every year in different sub-divisions of our country.
It helps them to compare and analyse the results. The table given below shows sub-division wise seasonal (monsoon) rainfall (mm) in 2018 :
Based on the above information, answer the following questions:
(i) Write the modal class. 1
(ii) Find the median of the given data. 2
OR
Find the mean rainfall in this season.
(iii) If sub-division having at least 1000 mm rainfall during monsoon season, is considered good rainfall sub-division, then how many sub-division had good rainfall ? 1
Solution:- See full solution