(i) If the lengths of the sides of a triangle are in the ratio 3: 4:5 and its perimeter is
48 cm, find its area.
(ii) The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300m
.Find its area. √3 = 1.732 .
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Answers
Answer:
(1) Given that the sides of a triangle are 3x,4x,5x.
Given that perimeter of a triangle = 48cm.
3x + 4x + 5x = 48
12x = 48
x = 4.
Then the sides of a triangle are:
3x = 3 * 4 = 12
4x = 4 * 4 = 16
5x = 5 * 4 = 20
We know that semi-perimeter of a triangle s = a + b + c/2
= (12 + 16 + 20)/2
= 48/2
= 24.
We know that Area of a triangle = \sqrt{s(s-a)(s-b)(s-c}
s(s−a)(s−b)(s−c
= \sqrt{24(24 - 12)(24 - 16)(24-20)}
24(24−12)(24−16)(24−20)
= \sqrt{24 * 12 * 8 * 4}
24∗12∗8∗4
= \sqrt{9216}
9216
= 96 cm^2.
(2) Given sides of the triangle are 3x,5x,7x
Given perimeter of a triangle = 300m.
3x + 5x + 7x = 300
15x = 300
x = 20.
Then the sides of the triangle are
3x = 3 * 20 = 60
5x = 5 * 20 = 100
7x = 7 * 20 = 140.
We know that semi-perimeter of a triangle s = (a + b + c)/2
= (60 + 100 + 140)/2
= 300/2
= 150m
We know that Area of a triangle = \sqrt{s(s-a)(s-b)(s-c)}
s(s−a)(s−b)(s−c)
= \sqrt{150(150 - 60)(150 - 100)(150 - 140)}
150(150−60)(150−100)(150−140)
= \sqrt{150 * 90 * 50 * 10}
150∗90∗50∗10
= \sqrt{(15 * 9 * 5) * (10)^4}
(15∗9∗5)∗(10)
4
= \sqrt{15 * 3 * 3 * 5 * 10^4}
15∗3∗3∗5∗10
4
= \sqrt{15 * (3 * 5) * 3 * 10^4}
15∗(3∗5)∗3∗10
4
= \sqrt{15 * 15 * 3 * 10^4}
15∗15∗3∗10
4
= \sqrt{(15)^2 * 3 * (10^2)^2}
(15)
2
∗3∗(10
2
)
2
= 15 * \sqrt{3} * (10)^215∗
3
∗(10)
2
= 1500\sqrt{3}1500
3
= 1500 * 1.732
= 2598.
Hope this helps!
Step-by-step explanation:
hope it helps you
(1) given ratio of lengths 3:4:5
=3x + 4x +5x = 48cm
12x = 48
X = 4
12cm , 16cm, 20cm are lengths of sides
using herons formula
A = √s ( s-a) ( s - b) (s - c)
s = 48/2= 24 cm
A = √24 (24 -12) (24-16) (24 -20)
√9216 = 96cm
(2) given ratio of lengths 3:5:7
= 3x + 5x + 7x = 300m
15x=300 ==> X = 20m
60m , 100m, 140m are lengths of sides of triangle
using herons formula for area
A = √(s-a) (s-b) (s-c)
s = 300/2 = 150
A ==
√300/2 (150-60) (150-100) (150-140)=
√6750000=2598.076m