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Geometry

Class Discussion: Geometry

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CAT 2025 Lesson : Class Discussion: Geometry - Quadrilaterals: 1 to 8

Class Discussion - Quadrilaterals

Question 1

A square, whose side is 2 metres, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres is
[CAT 2001]

		$\dfrac{\sqrt{2}}{\sqrt{2} + 1}$
		$\dfrac{2}{\sqrt{2} + 1}$
		$\dfrac{2}{\sqrt{2} - 1}$
		$\dfrac{\sqrt{2}}{\sqrt{2} - 1}$

Question 2

In the following figure, the area of the isosceles right triangle ABE is 7 sq.cm. If EC = 3BE, then the area of rectangle ABCD (in sq. cm.) is

[CAT 2002]

		64
		82
		26
		56

Question 3

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
[CAT 2002]

		$\dfrac{1}{2}$
		$\dfrac{2}{3}$
		$\dfrac{1}{4}$
		$\dfrac{3}{4}$

Question 4

Let

S_{1}

be a square of side a. Another square

S_{2}

is formed by joining the mid-points of the sides of

S_{1}

. The same process is applied to

S_{2}

to form yet another square

S_{3}

, and so on. If

A_{1}

A_{2}

A_{3}

... are the areas and

P_{1}

P_{2}

P_{3}

... are the perimeters of

S_{1}

S_{2}

S_{3}

... respectively, then the ratio

\dfrac{P_{1} + P_{2} + P_{3} + ...}{A_{1} + A_{2} + A_{3} + ...}

equals:
[CAT 2003 Retest]

		$\dfrac{2(1 + \sqrt{2})}{a}$
		$\dfrac{2(2 - \sqrt{2})}{a}$
		$\dfrac{2(2 + \sqrt{2})}{a}$
		$\dfrac{2(1 + 2\sqrt{2})}{a}$

Question 5

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?
[CAT 2004]

		5
		7
		9
		None of the above

Question 6

Rectangular tiles each of size 70 cm by 30 cm must be laid horizontally on a rectangular floor of size 110 cm by 130 cm, such that the tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum number of tiles that can be accommodated on the floor is
[CAT 2005]

		4
		5
		6
		7

Question 7

Which of the statements are required to answer the question below.
Rahim plans to draw a square JKLM with a point O on the side JK but is not successful. Why is Rahim unable to draw the square?
A. The Length of OM is twice that of OL
B. The length of OM is 4 cm.
[CAT 2007]

		Statement A alone and not B
		Statement B alone and not A
		Both statements together
		Either statement alone
		Neither of the statements are sufficient

Question 8

Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?
[CAT 2008]

		$\dfrac{4\sqrt{2}}{3}$
		$2 + \sqrt{3}$
		$\dfrac{10 - 3\sqrt{3}}{9}$
		$1 + \dfrac{1}{\sqrt{3}}$
		$2\sqrt{3} - 1$

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