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A playground is in the form of a rectangle having semicircles on the shorter sides. Find its area when the length of the rectangular portion is 80 m and the breadth is 42 m.
Radius of each of semicircle
= 42/2 = 21m
The required area =2 x area of semicircle EFA + area of rectangle ABDE
A playground which is 250 m long and 20 m broad is to be fenced with wire. How much wire is needed?
Clearly, the playground is of rectangular shape.
So the required length of the wire
= Perimeter of the rectangle
= 2 (length + breadth)
= 2 (250+20) = 540 m.
Given a triangle ABC in which BC = 6 cm, ∠ABC = 120° and AB = 7 cm. What is the name of the triangle which can be drawn from the given data?
Obtuse angled triangle as ∠ABC = 120°.
Varun purchased a book and sold it at a profit of 20% to Vijay. If Vijay paid? ₹ 1440 to Varun, then at what price did Varun buy the book?
Let C.P. = ₹ x
C.P. + 20% of C.P. = S.P.
= 240 x 5 = ₹ 1200
Three numbers A, B, and C are in the ratio 12 : 15 : 25. If the sum of these numbers is 312, then the ratio between the difference between B and A and the difference of C and B is
A : B : C = 12 : 15 :25
Total parts = 52
One part = 312/52 = 6
∴ A = 12 x 6 = 72, B = 15 x 6 = 90, C = 25 x 6 = 150
The ratio of the age of a father to that of his son is 5 : 2. If the product of their ages in years is 1000, then find the father’s age after 10 years.
Let father’s age = x years and son’s age be y years
According to question
Also; xy = 1000 .... (ii)
Put the value of y from Eqn. (i) in Eqn. (ii) we get
xy = 1000 ⇒ x × 2x/5 =1000 ⇒ 2x^{2} = 1000 × 5
⇒ x^{2} = 2500 ⇒ x = 50
So, after 10 years father’s age will be = x + 10
= 50+ 10 = 60 years.
If one angle of a triangle is equal to the sum of the other two angles, the triangle must be:
Let x, y and z is the angles, where x = y + z
x + y + z = 180° (angle sum property)
(y + z) + y + z = 180°
2(y + z)= 180°
x = 90°, hence triangle is right angled.
In the given figure, ∠a is greater than onesixth of the right angle, then:
As a > 1/6 (90°) => a > 15°
But a + b = 180° (linear Pair)
∴ b < 165°
If find y in terms of x and z?
⇒ 3x = y + z
⇒ 3 x  z = y
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
Total number of votes = 7500
Given that 20% of Percentage votes were invalid
⇒ Valid votes = 80%
Total valid votes = 7500*(80/100)
1st candidate got 55% of the total valid votes.
Hence the 2nd candidate should have got 45% of the total valid votes
⇒ Valid votes that 2nd candidate got = total valid votes x (45/100)
7500*(80/100)*(45/100) = 2700
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