Perimeter And Area - 2D Test

Result

Perimeter And Area - 2D Test - 2

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Question 1
1 / -0

The lengths of sides of a triangle are 5 units, 12 units and 13 units. A rectangle is constructed which is equal in area to the triangle. The rectangle has a length of 10 units. What is the perimeter of the rectangle?

A
30 units

B
36 units

C
13 units

D
None of these

Solution

Option (4) is the correct answer.
Question 2
1 / -0

A rectangular pool 20 m wide and 60 m long is surrounded by a walkway of uniform width. If the total area of the walkway is 516 m², how wide (in metres) is the walkway?

A
43

B
4.3

C
3

D
3.5

Solution

Let x be the width of the walkway.
Then, rectangle formed including walkway has
Length = 60 + 2x
Width = 20 + 2x

Area of rectangle including walkway = 60 x 20 + 516
(60 + 2x) (20 + 2x) = 1716 m²
X² + 40x - 129 = 0

(x + 43) (x - 3) = 0
X = 43 m x = 3 m
X = 43 is not possible.

Therefore, correct option is 3.
Question 3
1 / -0

Three identical cones with base radius r are placed on their bases such that each is touching the other two. What is the radius of the circle drawn through their vertices?

A
Smaller than r

B
Equal to r

C
Larger than r

D
Depends on the height of the cones

Solution

(Circle Radius) R > r
It is clear from the figure that radius of the circle drawn through the vertices is larger than the radius of base circle.

Hence, option (3) is the correct answer.