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Q:

The hypotenuse of a right-angled triangle 10 cm and its area is 24 cm^2. If the shorts side is halved and the longer side is double, the new hypotenuse becomes

A) √245 cm	B) √255 cm
C) √265 cm	D) √275 cm

Answer & Explanation Answer: C) √265 cm

Explanation:

Hypotenuse = 10cm

Let the other 2 perpendicular sides be a and b

Area ½ a*b = 24

So a*b = 48 cm^2

Also using Pythagoras

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Q:

The angles of a triangle are in the ratio 1 : 1 : 4. If the perimeter of the triangle is k times its largest side, then what is the value of k?

A) 1 + 2/√3	B) 1 - 2/√3
C) 2 + 2/√3	D) 2

Answer & Explanation Answer: A) 1 + 2/√3

Explanation:

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3 1502

Q:

A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle?

A) 12/π+4	B) 6/π+4
C) 3/π+4	D) 6/π+2√2

Answer & Explanation Answer: B) 6/π+4

Explanation:

As it is clear that 2r = a where a is the side of the square and

R is the radius of circle

It is given that 2πr + 4a = 12

a = 12/(π+4)

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1 1647

Q:

The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4 : 6, then what is the value of k?

A) 2	B) 3
C) 4	D) 5

Answer & Explanation Answer: C) 4

Explanation:

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1 1741

Q:

A rectangular red carpet of size 6 ft ×12 ft has a dark red border 6 inches wide. What is the area of the dark red border?

A) 9 square feet	B) 15 square feet
C) 17 square feet	D) 18 square feet

Answer & Explanation Answer: C) 17 square feet

Explanation:

Initially carpet is 6×12 = 72 sq feet

Since red border is 6 inches wide from all 4 side

So area without border = 5× 11 = 55 sq feet

Area of border = total–area without border = 72–55 = 17 sq feet

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Filed Under: Volume and Surface Area
Exam Prep: Bank Exams

1 1547

Q:

Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles?A. 154 square cmB. 308 square cmC. 462 square cmD. 616 square cm

A) 154 square cm	B) 308 square cm
C) 462 square cm	D) 616 square cm

Answer & Explanation Answer: C) 462 square cm

Explanation:

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Filed Under: Volume and Surface Area
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Q:

Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible?

A) Only one	B) Only two
C) Only three	D) Infinitely many

Answer & Explanation Answer: A) Only one

Explanation:

let n-1, n, n+1 be 3 consecutive integers

So

(n+1)^2= n^2+ (n-1)^2

(n+1)^2-(n-1)^2= n^2

4n = n^2

So n = 0 or n = 4

n can’t be 0 as n-1 will be negative then

So 3,4 and 5 is the only triplet formed.

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Filed Under: Volume and Surface Area
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Q:

The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?

A) a(√2 –1)	B) a(√3 –1)
C) a/√2+2	D) a/3

Answer & Explanation Answer: A) a(√2 –1)

Explanation:

Since we are forming a regular octagon

so AE = AL = FB = BG and so on

So AE = SB = x/√2

AE + EF + FB = side of square = a (Given)

So x/√2 + x + x/√2 = a

X = a/(√2+1) = a(√2 -1)

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Filed Under: Volume and Surface Area
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