Question

Q.20 Case Study 4-
a) 1320 sq.m
The triangular side walls of a flyover have been used for advertisements. The sides of the walls are
122 m, 22 m and 120 m. The advertisements yield an earning of Rs.7000 per m per year.
1. What is the semi perimeter of each wall?
a) 16 m
b) 528 m
e) 264 m
d) 132 m
2. What is the area of each wall?
b) 2640 sq.m
c) 660 sq.m
none of these
3. A company hired one of its walls for six months. How much rent did it pay?
a) Rs.9240000
c) Rs.4620000
d) Rs. 3080000
4. If an altitude is drawn on the smallest side of the triangular wall, what will be the length of this
altitude?
a) 60m
b) 120m
c) 130m
d) 240m
5. What is the cost of fencing each wall at the rate of Rs. 4.50 per m.
a) Rs.5962.5
b) Rs. 1188
c) Rs.660
d) None of these
b) Rs.7000​

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

sides of a triangular wall have dimensions, 120 m, 22 m and 122 m.

Let assume that

a = 120 m

b = 22 m

c = 122 m.

Now,

Consider,

$\rm :\longmapsto\: {a}^{2} + {b}^{2}$

$\rm \: \: = \: {(120)}^{2} + {(22)}^{2}$

$\rm \: \: = \: 14400 + 484$

$\rm \: \: = \: 14884$

$\rm \: \: = \: {(122)}^{2}$

$\rm \: \: = \: {c}^{2}$

It implies, triangle is right angled triangle.

Answer:- 1

Semi-perimeter of one side of triangular wall is

$\rm \: \: = \: \dfrac{1}{2}(a + b + c)$

$\rm \: \: = \: \dfrac{1}{2}(120 + 22 + 122)$

$\rm \: \: = \: \dfrac{1}{2}(264)$

$\rm \: \: = \: 132 \: m$

Option (d) is correct.

Answer:- 2

Area of each wall,

$\rm \: \: = \: \dfrac{1}{2} \times a \times b$

$\rm \: \: = \: \dfrac{1}{2} \times 22 \times 120$

$\rm \: \: = \: 1320 \: {m}^{2}$

Option (a) is correct

Answer:- 3

Rent per square meter of wall for 12 months = Rs 7000

So,

Rent per square meter of wall for 6 months = Rs 3500

Therefore, rent for 6 months is

$\rm \: \: = \: 1320 \times 3500$

$\rm \: \: = \: Rs \: 4620000$

Option (c) is correct

Answer :- 4

Let height of altitude be 'h' m

Since, Area of triangle = 1320 square meter.

$\rm :\longmapsto\:1320 = \dfrac{1}{2} \times h \times 22$

$\rm :\longmapsto\:1320 = h \times 11$

$\rm :\longmapsto\: h = 120 \: m$

Option (b) is correct

Answer :- 5

Cost of fencing per meter = Rs 4.5 m

Cost of fencing per meter = 4.5 (a + b + c)

$\rm \: \: = \: 4.5 \times (120 + 22 + 122)$

$\rm \: \: = \: 4.5 \times (264)$

$\rm \: \: = \: Rs \: 1188$

Option (b) is correct