RD Sharma Solutions for Class 9 Maths are given here for Chapter 12 exercise 12.1. In this exercise, students will learn how to find the area of a triangle using heron’s formula with the help of various solved examples.
Heron’s Formula:
The Solutions for RD Sharma class 9 Maths chapter 12 exercise 12.1 includes solved problems and step by step explanations given by our experts to further helps students find alternative ways to solve a problem.
RD Sharma Solutions for Class 9 Maths Chapter 12 Heron’s Formula Exercise 12.1
Access Answers to Maths RD Sharma Class 9 Chapter 12 Heron’s Formula Exercise 12.1 Page number 12.8
Question 1: Find the area of a triangle whose sides are respectively 150 cm, 120 cm and 200 cm.
Solution:
We know, Heron’s Formula
Here, a = 150 cm
b = 120 cm
c = 200 cm
Step 1: Find s
s = (a+b+c)/2
s = (150+200+120)/2
s = 235 cm
Step 2: Find Area of a triangle
= 8966.56
Area of triangle is 8966.56 sq.cm.
Question 2: Find the area of a triangle whose sides are respectively 9 cm, 12 cm and 15 cm.
Solution:
We know, Heron’s Formula
Here, a = 9 cm
b = 12 cm
c = 15 cm
Step 1: Find s
s = (a+b+c)/2
s = (9 + 12 + 15)/2
s = 18 cm
Step 2: Find Area of a triangle
= 54
Area of triangle is 54 sq.cm.
Question 3: Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.
Solution:
Given:
a = 18 cm, b = 10 cm, and perimeter = 42 cm
Let c be the third side of the triangle.
Step 1: Find third side of the triangle, that is c
We know, perimeter = 2s,
2s = 42
s = 21
Again, s = (a+b+c)/2
Put the value of s, we get
21 = (18+10+c)/2
42 = 28 + c
c = 14 cm
Step 2: Find area of triangle
Question 4: In a triangle ABC, AB = 15cm, BC = 13cm and AC = 14cm. Find the area of triangle ABC and hence its altitude on AC.
Solution:
Let the sides of the given triangle be AB = a, BC = b, AC = c respectively.
Here, a = 15 cm
b = 13 cm
c = 14 cm
From Heron’s Formula;
= 84
Area = 84 cm2
Let, BE is a perpendicular on AC
Now, area of triangle = ½ x Base x Height
½ × BE × AC = 84
BE = 12cm
Hence, altitude is 12 cm.
Question 5: The perimeter of a triangular field is 540 m and its sides are in the ratio 25:17:12. Find the area of the triangle.
Solution:
Let the sides of a given triangle be a = 25x, b = 17x, c = 12x respectively,
Given, Perimeter of triangle = 540 cm
2s = a + b + c
a + b + c = 540 cm
25x + 17x + 12x = 540 cm
54x = 540 cm
x = 10 cm
So, the sides of a triangle are
a = 250 cm
b = 170 cm
c = 120 cm
Semi perimeter, s = (a+b+c)/2
= 540/2
= 270
s = 270 cm
From Heron’s Formula;
= 9000
Hence, the area of the triangle is 9000 cm2 .
RD Sharma Solutions for Class 9 Maths Chapter 12 Exercise 12.1
Class 9 Maths Chapter 12 Heron’s Formula Exercise 12.1 is based on Heron’s formula. Find detailed RD Sharma solutions for class 9 Maths chapter 12, solved by BYJU’S experts using step-by-step problem solving method here. Students can freely download RD Sharma solutions and sharpen their skills.
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