CAT 2025 Lesson : Class Discussion: Geometry - Lines & Triangles: 1 to 8

Class Discussion – Lines and Triangles

Question 1

What is the number of distinct triangles with integral valued sides and perimeter 14?
[CAT 2000]

		3
		4
		5
		6

Question 2

In the below diagram, ABCD is a rectangle with AE = EF = FB. What is the ratio of the area of the triangle CEF and that of the rectangle?
[CAT 2001]

		$\dfrac{1}{6}$
		$\dfrac{1}{8}$
		$\dfrac{1}{9}$
		None of these

Question 3

A ladder leans against a vertical wall. The top of the ladder is 8 m above the ground. When the bottom of the ladder is moved 2 m farther away from the wall, the top of the ladder rests against the foot of the wall. What is the length of the ladder?
[CAT 2001]

		10 m
		15 m
		20 m
		17 m

Question 4

Euclid has a triangle in mind, Its longest side has length 20 and another of its sides has length 10. Its area is 80. What is the exact length of its third side?
[CAT 2001]

		$\sqrt{260}$
		$\sqrt{250}$
		$\sqrt{240}$
		$\sqrt{270}$

Question 5

A piece of paper is in the shape of a right angled triangle and is cut along a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 square inches before the cut, what is the area (in square inches) of the smaller triangle?
[CAT 2003 Retest]

		16.665
		16.565
		15.465
		14.365

Question 6

In the figure (not drawn to scale) given below, if AD = CD = BC, and ∠BCE = 96°, how much is

\angle

DBC?

		$32\degree$
		$84\degree$
		$64\degree$
		Cannot be determined

Question 7

A father and his son are waiting at a bus stop in the evening. There is a lamp post behind them. The lamp post, the father and his son stand on the same straight line. The father observes that the shadows of his head and his son's head are incident at the same point on the ground. If the heights of the lamp post, the father and his son are 6 metres, 1.8 metres and 0.9 metres respectively, and the father is standing 2.1 metres away from the post, then how far (in metres) is the son standing from his father?
[CAT 2004]

		0.9
		0.75
		0.6
		0.45

Question 8

If the lengths of diagonals DF, AG and CE of the cube shown in the adjoining figure are equal to the three sides of a triangle, then the radius of the circle circumscribing that triangle will be
[CAT 2004]

		equal to the side of the cube
		$\sqrt{3}$ times the side of the cube
		$\dfrac{1}{\sqrt{3}}$ times the side of the cube}
		Impossible to find from the given information

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