### CAT Mensuration Practice Exercise-3

CAT Mensuration questions revolve mostly around 2 important shapes i.e. circles and triangles. Here are some questions based on the concepts of triangle and its types. The key concepts that you need to know for these CAT Mensuration questions are:

- Types of triangles
- Angle and length properties for triangles
- Formulas for finding area and perimeter for different types of triangles

**Question 1:** If the numerical value of the peÂ¬rimeter of an equilateral triangle is âˆš3 times the area of it. What is the length of each side of the triÂ¬angle?

(a) 2 unit

(b) 3 unit

(c) 4 unit

(d) 6 unit

### Answer and Explanation

Answer: (c)

The side of the equilateral triangle be a units.

**Question 2:** Each side of an equilateral triangle is 6 cm. Find out its area.

(a) 9âˆš3 sq.cm.

(b) 6âˆš3 sq.cm.

(c) 4âˆš3 sq.cm.

(d) 8âˆš3 sq.cm.

### Answer and Explanation

Answer: (a)

**Question 3:** If a circle with radius 8 cm has same area as triangle with base 8 cm, then find the correÂsponding altitude (in cm) of the triangle.

(a) 12Ï€

(b) 20Ï€

(c) 16Ï€

(d) 32Ï€

### Answer and Explanation

Answer: (c)**
**

Assume the corresponding altitudes of the triangle = a cm

According to the question,

Area of the triangle = Area of the circle

1/2 x base x height=Ï€ x radius x radius

â‡’ 1/2 x a Ã— 8 = Ï€ Ã— 8 Ã— 8

â‡’ a = 2 Ã— 8Ï€ = 16Ï€ cm.

**Question 4:** The measures (in cm) of sides of a right angled triangle are given by consecutive integers. What is its area (in cm^{2})?

(1) 9

(2) 8

(3) 5

(4) 6

### Answer and Explanation

Answer: (d)

Only right angle triangle with consecutive integers is with side 3,4 and 5.

3^{2} + 4^{2} = 5^{2}

âˆ´Â Â Base = 3 cm;

Perpendicular = 4 cm

âˆ´Â Â Area of the right angled triangle

= 1/2 Ã— base Ã— height

= 1/2 Ã— 3 Ã— 4 = 6 sq. cm.

**Question 5**: Sides of a triangle are in the ratio 1/3:1/4:1/5and its perimeter is 94cm. Find the length of the largest side of the triangle?

(a) 18cm

(b) 22.5 cm

(c) 24 cm

(d) 27 cm

### Answer and Explanation

Answer: (c)

**Extra tips for CAT Mensuration Questions:**

- In order to solve CAT Mensuration questions, revise the basic concepts of triangles and its types- Right angled, equilateral, isosceles, scalene, etc. Each type has different formulas and triangle itself has a set of general formulas for finding different parameters. You can equate these formulas to simplify the solutions in some questions.
- Identify the type of triangle and define the variables appropriately. These type CAT Mensuration questions can also be solved without drawing any diagrams.
- Problems based on sizing the sides as ratios can be solved by simplifying the ratios and then solving using the given parameter.