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Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT PDF Download

From a given perimeter how many triangles with integral sides are possible?

We can solve this question within seconds with the help of a tips and tricks. Generally there are two cases for these type of questions. 

Scenario 1:

When Perimeter is odd

Scenario 2:

When perimeter is even

Scenario 1 – Details

  • How many triangles with integral sides are possible for perimeter P where P is even

Solution – In this case, total number of triangles will be the nearest integer to P2/48 

Scenario 2 – Details

  • How many triangles with integral sides are possible for perimeter P where P is odd

Solution – In this case, total number of triangles will be the nearest integer to Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT 

Tips and Tricks on Geometry

Q1: ABCD is a square. AD is tangent to circle with radius r and OE = ED. Then what is the ratio of the area of circle to the area of square?

Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT(a) π/3
(b) πr2/3
(c) πr2/4
(d) 2πr/4r
Ans:
a
Sol:
OD2 = OA2+ AD2

(2r)2 = r2 + AD2

Thus PQ, which is also the side of square, is equal to r√3. The area of square becomes:  3r2
Hence the ratio of the area of circle to square is: 

Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT

Correct Option (A)

Q2: If in a triangle ABC, Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT then what can be said about the triangle ?
(a) Right angled triangle
(b) Isosceles triangle
(c) Equilateral triangle
(d) Nothing can be inferred

Ans: c
Sol:
From the sine rule of triangle we know,Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT
Therefore, a = k(sin A), b = k(Sin B) and c = k(Sin C)

Hence, we can rewrite, Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT
or Cot A= Cot B= Cot C
A = B = C, Hence the triangle is equal.
Correct Option (C)

The document Geometry: Shortcuts & Tricks | Quantitative Techniques for CLAT is a part of the CLAT Course Quantitative Techniques for CLAT.
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