Selina Concise Class 9 Maths Chapter 20 Area and Perimeter Of A Plane Figures Exercise 20D Solutions
EXERCISE – 20D
(1) The Perimeter of a triangle is 450 cm and it’s side are in the ratio 12: 5: 13. Find the area of the triangle.
Solution:
Given: The perimeter of a triangle is 450 cm.
Perimeter = 450
12x + 5x + 13x = 450
(Perimeter = Sum of all sides of a triangle)
30x = 450
X = 450/30
X = 15
Height = 12 x = 12 × 15 = 180 m.
Base = 5x = 5 × 15 = 75 m
Area of a triangle = 1/2 × Base × height
= 1/2 × 75 × 180
= 75 × 40
= 6750 m2
(2) A triangle and a parallelogram have the same base and the same area. If the side of the triangle are 26cm, 28cm, and 30cm, and the parallelogram stands on the base 28cm, find the height of the parallelogram.
Solution:
In △ABC,
S = 30 + 28 + 26/2
= 84/2
S = 42
Area (△ABC) = √S (s – a ) (s – b) (s – c)
= √42 (42 – 30) ( 42 – 28) (42 – 26)
= √42 × 12 × 14 × 16
= √14 × 3 × 2 × 2 × 3 × 14 × 2 × 2 × 2
= 14 × 3 × 2 × 2 × 2
= 14 × 3 × 8
Area (BCDE) = 14 × 3 × 8
Base × Height = 14 × 3 × 8
26 × Height = 14 × 3 × 8
Height = 14 × 3 × 8/ 26
Height = 12 cm
∴ The height of the parallelogram is 12 cm.
(3) Using the information in the following figure, find it’s area.
Solution:
In △BEC,
BY Pythagoras Theorem,
BC2 = CE2 + BE2
(15)2 = (9)2 + BE2
225 = 81 + BE2
225 – 81 = BE2
144 = BE2
Taking Square root on both sides,
√144 = √BE2
12m = BE
∴ AB = 23 + 12 = 35m
Area of (ABCD) = 1/2 ( Sum of parallel sides × height)
= 1/2 (35 + 23) × 9
= 1/2 × 58 × 9
= 29 × 9
= 261 m2
∴ Area of parallelogram ABCD is 261 m2.
(4) Sum of the areas or two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.
Solution:
A2 + a2 = 400 —–(i)
If the difference of their perimeters is 16cm.
4A – 4a = 16
4 (A – a) = 16
A – a = 16/4
A = 4 + a
Put in equation we get (i),
(4 + a)2 + a2 = 400
(4)2 + 2 × 4 × a + a2 + a2 = 400
16 + 8a + a2 + a2 = 400
16 + 8a + 2a2 = 400
2a2 + 8a + 16 – 400 = 0
2a2 + 8a – 384 = 0
2 (a2 + 4a – 192) = 0
a2 + 4a – 192 = 0
a2 + 16a – 12a – 192 = 0
a (a + 16) – 12 (a + 16) = 0
(a + 16) (a – 12) = 0
a + 16 = 0 or a – 12 = 0
a = -16 or a = 12
∴ a = 12 cm.
∴ A = 4 + a
= 4 + 12
A = 16 cm.
∴ The two sides of a square are 12cm and 16 cm.
(5) Find the area and the perimeter, of a square with diagonal 24cm. (Take √2 = 1.41)
Solution:
Given the perimeter of a square with diagonal 24 cm.
Diagonal = 24 cm.
a √2 = 24
a = 24/√2
a = 24/√2 × √2/√2
a = 24 × √2/ 2
a = 12 √2 cm.
Area of a Square = (Side)2
= a2
= (12 √2)2
= 144 × 2
= 288 cm2
Perimeter of a = 4 a
= 4 × 12√2
= 48√2
= 48 × 1.41
= 67. 68 cm
∴ The area of a Square is 288cm2 and the perimeter of a Square is 67.68 cm.
Here is your solution of Selina Concise Class 9 Maths Chapter 20 Area and Perimeter Of A Plane Figures Exercise 20D
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