NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.1
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s
Formula Ex 12.1 are the part
of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for
Chapter 12 Heron’s
Formula Ex 12.1.
Ex 12.1 Class 9 Maths Question 1.
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 180 cm, what will be
the area of the signal board?
Solution:
We know that, an equilateral
triangle has equal sides. So, all sides are equal to a.
Perimeter
of the triangle = 180 cm
⇒ a + a + a = 180
⇒ 3a = 180
⇒ a = 60 cm
Now,
semi-perimeter (s) = (a + a + a)/2
(∵ 2s = a +
b + c)
s =
180/2 = 90 cm
Ex 12.1 Class 9 Maths Question 2.
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 (see Fig.). The advertisements yield an earning of Rs. 5000 per m2 per
year. A company hired one of its walls for 3 months. How much rent did it pay?
Solution:
The lengths of the sides of the triangular walls are 122 m, 22 m and 120 m.
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 15 m, 11 m and 6 m,
find the area painted in colour.
Solution:
Ex 12.1 Class 9 Maths Question 4.
Find the area of a triangle two
sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:
Let the sides of the triangle be a
=18 cm, b = 10 cm and c = x cm
Since, perimeter of the triangle = 42 cm
∴ 18 cm + 10 cm + x cm = 42
x = [42 – (18 + 10) cm = 14 cm
Now, semi-perimeter, s = 42/2 = 21 cm
Ex 12.1 Class 9 Maths Question 5.
Sides of a triangle are in the
ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
Solution:
Let the sides of the triangle be a
= 12x cm, b = 17x cm and c = 25x cm
Perimeter of the triangle = 540 cm
Now, 12x + 17x + 25x = 540
⇒ 54x = 540 ⇒ x = 10
∴ a = (12 × 10) cm = 120 cm,
b = (17 × 10) cm = 170 cm
and c = (25 × 10) cm = 250 cm
Now, semi-perimeter, s = 540/2 = 270 cm
Ex 12.1 Class 9 Maths Question 6.
An isosceles triangle has perimeter 30 cm and each
of the equal sides is 12 cm. Find the area of the triangle.
Solution:
Let the sides of an isosceles triangle be a = 12 cm,
b = 12 cm and c = x cm
Since, perimeter of the triangle = 30 cm
∴ 12 cm + 12 cm + x cm = 30 cm
⇒ x = (30 – 24) = 6 cm
Now, semi-perimeter, s = 30/2 =15 cm
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