9th Maths 12.1

NCERT Class 9th solution of Exercise 12.1

Exercise 12.1

Q1. A traffic signal board, indicating 'SCHOOL AHEAD', is an equilateral triangle with side 'a'. Find the area of the signal board, using Heron's formula. If its perimeter is 180cm, what will be the area of the signal board?
Sol. :
Semi persmeter S=a+a+a2=3a2
By Heron's formula: 
Area of =S(S-a)(S-b)(S-c)
Area of =3a2(3a2-a)(3a2-a)(3a2-a)
Area of =3a2(a2)(a2)(a2)
Area of =34a2 square unit.
The Perimeter of equilateral =3a
180=3a
a=1803
a=60
Area of =34a2
Area of =(60)243cm2
Area of =60×6043cm2
Area of =9003cm2
Answer :
Area of the signal board =9003cm2.
Q2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m,22m and 120m[see figure]. The advertisements yield an earning of 5000 per m2per year. A company hired one of its walls for 3 months. How much rent did it pay?
Sol. :
Let side a=122m,b=120m and c=22m
S=a+b+c2
S=122+120+222
S=2642
S=132
By Heron's  formula:
Area of =S(S-a)(S-b)(S-c)
Area of =132(132-122)(132-120)(132-22)
Area of =132(10)(12)(110)
Area of =11×12×10×12×11×10
Area of =10×11×12
Area of =1320m2
Rent for 3 months = Area×Rate
    =1320×5000×312
    =110×15000
    =165000
Answer:
Rent for 3 months 165000.
Q3. There is a slide in a park. One of its side walls has been painted in some colour with a message '' KEEP THE PARK GREEN AND CLEAN'' [see figure]. If the sides of the wall are 15m, 11m, and 6m. find the area painted in colour.
Sol. :
Let side a=15m,b=11m and c=6m
S=a+b+c2
S=15+11+62
S=322
S=16m
By Heron's formula:
Area of =S(S-a)(S-b)(S-c)
Area of =16(16-15)(16-11)(16-6)
Area of =16×1×5×10
Area of =4×4×5×5×2
Area of =4×52m2
Area of =202m2
Answer:
The area of painted in colour 202m2.
Q4. Find the area of a triangle two sides of which are 18cm and 10cm the perimeter is 42cm.
Sol. :
Let side a=18cm,b=10cm
Perimeter of =a+b+c
42=18+10+c
c=42-28
c=14
S=422
S=21
By Heron's formula:
Area of =S(S-a)(S-b)(S-c)
Area of =21(21-18)(21-10)(21-14)
Area of =21×3×11×7
Area of =2111cm2
Answer:
Area of =2111cm2.
Q5. Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540cm. Find its area.
Sol. :
Let side a=12x,b=17x and c=25x
Perimeter of =a+b+c
540=12x+17x+25x
540=54x
x=54054
x=10
a=12×10=120
b=17×10=170
c=25×10=250
S=5402=270
Area of =S(S-a)(S-b)(S-c)
Area of =270(270-120)(270-170)(270-250)
Area of =270×150×100×20
Area of =9000cm2
Answer:
Area of =9000cm2.
Q6. An isosceles triangle has perimeter 30cm and each of the equal sides is 12cm. Find the area of the triangle.
Sol. :
Let side a=12, b=12`
Perimeter of =a+b+c
30=12+12+c
c=30-24
c=6
S=302=15
By Heron's formula:
Area of =S(S-a)(S-b)(S-c)
Area of =15(15-12)(15-12)(15-6)
Area of =15×3×3×9
Area of =915
Answer:
Area of =915cm2.

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