The ratio of heights of two triangles is 2 : 3 and the ratio of their areas 3 : 2. The ratio of their bases is :

1. 1 : 4

2. 2 : 8

3. 9 : 4

4. 4 : 9

The perimeter of a rectangle is 26 m. If the length of the rectangle is 3 m more than its breadth, then its area will be :

1. 36 m²

2. 38 m²

3. 40 m²

4. 42 m²

Case Study:
In most of the Indian metropolitan cities, government has made many flyovers to regulate the traffic flow. One of such flyover is shown below. The triangular side walls of the flyover have been used for advertisements. One of such side walls has lengths 122 m, 120 m and 22 m. The rate of advertisement on this wall is ₹ 1,000 per m² per year. A private company hired this wall for 4 months.

Based on the above information, answer the following questions:

1. Semi-perimeter of the triangular wall is :
   (a) 130 m
   (b) 132 m
   (c) 134 m
   (d) 135 m

2. Area of the triangular wall is :
   (a) 1400 m²
   (b) 1350 m²
   (c) 1340 m²
   (d) 1320 m²

3. Total amount paid by the company as rent for the wall is:
   (a) ₹4,00,000
   (b) ₹4,20,000
   (c) ₹4,40,000
   (d) ₹13,20,000

4. Another company paid ₹5,50,000 as a rent for the same wall. For how many months did the company hire the wall?
   (a) 5
   (b) 6
   (c) 7
   (d) 8

5. Which of the following is the correct formula for finding the area of a triangle of sides x, y, z and semi perimeter p?
   (a) Area = p(p - x) (p - y) (p - z)
   (b) Area = $\sqrt{p(p + x)(p + y)(p + z)}$
   (c) Area = $\sqrt{(p - x)(p - y)(p - z)}$
   (d) Area = $\sqrt{p(p - x)(p - y)(p - z)}$

Assertion (A): Length of the diagonal of a square field is $15\sqrt{2}$ m. Cost of ploughing the field at ₹20 per m² is ₹4,500.

Reason (R): $\text{Area of a Square} = \dfrac{(\text{Diagonal})^2}{4}$

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false