If the area, perimeter and diameter of a circle are a,b and c then show that bc=4a
Answers
Answer:
Step-by-step explanation:
⇒ Here, AB=BC=AC=12cm
⇒ Let OP=OR=OQ=r
⇒ We have O as the incenter and OP,OQ and OR are equal.
⇒ ar(△ABC)=ar(△OAB)+ar(△OBC)+ar(△OCA)
4
3
×(side)
2
=(
2
1
×OP×AB)+(
2
1
×OQ×BC)+(
2
1
×OR×AC)
⇒
4
3
×(12)
2
=(
2
1
×r×12)+(
2
1
×r×12)+(
2
1
×r×12)
⇒
4
3
×(12)
2
=3(
2
1
×12×r)
∴ r=
18
36
3
∴ r=2
3
cm
⇒ Area of the shaded region = Area of △ABC - Area of circle.
⇒ Area of the shaded region =
4
3
×(12)
2
−
7
22
×(2
3
)
2
⇒ Area of the shaded region =(62.35−37.71)cm
2
=24.64cm
2
ML Aggarwal Solutions for Class 9 Maths Chapter 16 Mensuration is an important study material for the students from the exam perspective. Students can refer to the solutions designed by the subject matter experts at BYJU’S having vast conceptual knowledge. The main aim of providing ML Aggarwal Solutions for Class 9 Maths Chapter 16 Mensuration PDF is to boost the exam preparation of students.
Chapter 16 consists of problems on finding the area of various figures like triangles, polygons, etc. The ML Aggarwal Solutions help students understand the concepts and their applications in a wide range. Each problem is solved after conducting wide research on the concepts to help students, irrespective of their intelligence quotient.
Access ML Aggarwal Solutions for Class 9 Maths Chapter 16: Mensuration
Exercise 16.1
1. Find the area of a triangle whose base is 6 cm and corresponding height is 4 cm.
Solution:
It is given that
Base of triangle = 6 cm
Height of triangle = 4 cm
We know that
Area of triangle = ½ × base × height
Substituting the values
= ½ × 6 × 4
By further calculation
= 6 × 2
= 12 cm2
2. Find the area of a triangle whose sides are
(i) 3 cm, 4 cm and 5 cm
(ii) 29 cm, 20 cm and 21 cm
(iii) 12 cm, 9.6 cm and 7.2 cm
Solution:
(i) Consider a = 3 cm, b = 4 cm and c = 5 cm
We know that
S = Semi perimeter = (a + b + c)/ 2
Substituting the values
= (3 + 4 + 5)/ 2
= 12/2
= 6 cm
Answer:
I have attached the answer sheet
