☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️☣️ 6. The sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is
84 cm. Find the area of the triangle.
7. Find the area of A ABC in which BC =8 cm, AC = 15 cm and AB = 17 cm. Find the length of altitude drawn on AB.
8. An isosceles triangle has perimeter 30 cm and each of its equal sides is
12 cm. Find the area of the triangle.
9. The perimeter of an isosceles triangle is 32 cm. The ratio of one of the equal sides to its base is 3:2. Find the area of the triangle.
Answers
Answer:
Step-by-step explanation:
(6) Let the sides of the triangle be 13x,14x and 15x.
Therefore, 13x+14x+15x=84
42x=84
x=2
Hence, sides of the triangle are 26 cm , 28 cm & 30 cm.
Area of the triangle =√s*(s-a)*(s-b)*(s-c).
[Heron's Formula]
s=a+b+c/2=26+28+30/2= 84/2=42.
a=26cm
Area=√42*(42-26)*(42-28)*(42-30).
b=28 cm
Area=√42* 16*14*12. c=30 cm
Area=√42*2688
Area=√112896
Area=336 cm²
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(7) Let the sides be 13x, 14x and 15x
Perimeter = Sum of all sides
84 = 13x + 14x + 15x
42x = 84
x = 2
So, the sides are a = 26 cm, b = 28 cm and c = 30 cm
s = p/2 = 84/2 = 42 cm
Area = √s(s - a)(s - b)(s - c)
= √42(42 - 26)(42 - 28)(42 - 30)
= √42*16*14*12
= 4√14*14*36
= 4*14*6
= 336 cm^2
So, area of triangle = 336 cm^2
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(8) Semi perimeter = s
s =( AB +BC + AC)/2
s = (17 + 8 + 15)/2 = 40/2 = 20cm
By Heron's formula, area of triangle ABC,
Area = √s(s-a)(s-b)(s-c)
= √20 (20 - 17) (20 - 8) (20 - 15)
= √20 (3 x 12 x 5)
= √20 x 180
= √3600 = 60cm²
Again area of triangle = 1/2 base x height\
60 = 1/2 x 17 x h
h = 120/17
h = 7.05cm
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(9) Let The Third Side Be xcm.
Now Perimeter = 12+12+x
24+x = 30
x = 6
Now Find The Area Using Herons Formula
Semiperimeter = 30/2 = 15
Sq Root(15(15-12)(15-12)(15-6) ) = Sq Root(15*3*3*9) = Sq Root(1215) = 34.85 cm^2
So Area is 34.85cm^2
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the perimeter of isosceles triangle = 32cm
p of isosceles triangle = 2 * equal side + base
let length of equal side be 3x and base be 2x
then
2 * 3x + 2x = 32 cm
6x + 2x = 32cm
8x = 32 cm
x= 4 cm
length of equal side = 3*4= 12cm
length of base = 2*4=8cm
area of isosceles triangle=b*1/4*√4a2-b2
= 8*1/4√4*144-64
=2√512
=2*22.62
= 45.25cm2
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Hope it helps
:)