December 30th, 2019 by Ravi Handa

Quantitative Aptitude - Geometry - Triangles - From a triangle ABC with sides
Quantitative Aptitude - Geometry - Triangles
Question
From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is
A) 225âˆš3
B) 500 / âˆš3
C) 275 / âˆš3
D) 250 / âˆš3
Answer
Option (B)
Solution
As per the question from CAT 2017 - Quantitative Aptitude - Geometry - Triangles,
Area of triangle = root (s(s-a)(s-b

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December 23rd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Mensuration â€“ A parallelogram ABCD has area 48 sqcm
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ A parallelogram ABCD has area 48 sqcm
A parallelogram ABCD has area 48 sqcm. If the length of CD is 8 cm and that of AD is s cm, then which one of the following is necessarily true?
a) 5â‰¤sâ‰¤7
b) sâ‰¤6
c) sâ‰¥6
d) sâ‰ 6
Answer: c) sâ‰¥6
Solution: 1
Solution: As the area of ABCD = 48=sÃ—h ------------1)
In right-angled triangle CKD, DK â‰¤ CD ( CD is hyp

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December 23rd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Mensuration â€“ The area of a rectangle and the square
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ The area of a rectangle and the square
The area of a rectangle and the square of its perimeter are in the ratio 1 âˆ¶ 25. Then the lengths of the shorter and longer sides of the rectangle are in the ratio?
a) 1:3
b) 3:8
c) 2:9
d) 1:4
Answer: d) 1 : 4
Solution:
Given ratio of areas of rectangle and square = 1:25 = 4âˆ¶ 100=(1Ã—4):(10Ã—10)
Thus possible ratio

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December 23rd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Triangles â€“ A triangle ABC has area 32 sq units
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Triangles â€“ A triangle ABC has area 32 sq units
A triangle ABC has area 32 sq units and its side BC, of length 8 units, lies on the line x = 4. Then the shortest possible distance between A and the point (0,0) is?
a) 4âˆš2 units
b) 8 units
c) 4 units
d) 2âˆš2 units
Answer: c) 4 units
Solution: The distance OA will be minimum when the perpendicular from A on BC will pass through O.

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December 22nd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Circles â€“ A chord of length 5 cm subtends an
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Circles â€“ A chord of length 5 cm subtends an
A chord of length 5 cm subtends an angle of 60Â° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120Â° at the centre of the same circle is?
a) 6âˆš2
b) 8
c) 4âˆš2
d) 5âˆš3
Answer: d) 5âˆš3
Solution:
In triangle ODA, OA=AD cosec 30=5
So if the angle AOB is 120 degree, then angle AOD will be 120/2=60

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December 22nd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Triangles â€“ On a triangle ABC, a circle with diameter BC
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Triangles â€“ On a triangle ABC, a circle with diameter BC
On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is?
Answer: 24 cm
Solution:
As CP is perpendicular to AB and BQ is perpendicular to AC. So
ABÃ—CP=ACÃ—BQ

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December 22nd, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Rectangle â€“ From a rectangle ABCD of area 768 sq cm
Slot -2 â€“Â Quantitative Aptitude â€“ Geometry - Rectangle â€“ From a rectangle ABCD of area 768 sq cm
From a rectangle ABCD of area 768 sq cm, a semicircular part with diameter AB and area 72Ï€ sq cm is removed. The perimeter of the leftover portion, in cm, is?
a) 88 + 12Ï€
b) 82 + 24Ï€
c) 80 + 16Ï€
d) 86 + 8Ï€
Answer: a) 88 + 12Ï€
Solution:
Given area of semicircle = 72Ï€
Or (Ï€r^2)/2 = 72Ï€
r = 12
So AB = 24

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December 21st, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Polygons â€“ In a parallelogram ABCD of area 72 sq cm
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Polygons â€“ In a parallelogram ABCD of area 72 sq cm
In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is?
a) 24âˆš3
b) 12âˆš3
c) 32âˆš3
d) 18âˆš3
Answer: c) 32âˆš3
Solution:
As given, Area of parallelogram ABCD = 72
So AB

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December 21st, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Mensuration â€“ Let ABCD be a rectangle inscribed in a circle
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Mensuration â€“ Let ABCD be a rectangle inscribed in a circle
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
a) 25, 10
b) 24, 12
c) 25, 9
d) 24, 10
Answer: d) 24, 10
Solution:
As ABCD is a rectangle angles A,B,C and D will be 90Â°. Thus AC will be diameter of

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December 21st, 2019 by Ravi Handa

Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle with center O and radius 1 cm
Slot -1 â€“Â Quantitative Aptitude â€“ Geometry - Circles â€“ In a circle with center O and radius 1 cm
In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is?
a) (Ï€/6)^(1/2)
b) (Ï€/(4âˆš3))^(1/2)
c)

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