Find the area of a triangle whose sides are in the ratio of 3 : 5 : 7 and its perimeter is 300 cm.
Answers
Step-by-step explanation:
Let the sides be 3x, 5x and 7x
3x+5x+7x = 15x
Perimeter is sum of all sides
So,
15x = 300
x = 20
Now the sides are equal to:
3x = 3* 20 = 60 cm
5x = 100 cm
7x = 140 cm
Now apply Heron's Formula for the rest of the Q.
Formula of Heron's Formula =
s = 150
a = 60
b = 100
c = 140
Step-by-step explanation:
Let the sides of a triangle be x
a = 3x
b = 5x
c. = 7x
perimeter =300cm
3x + 5x + 7x = 300cm ( add all the values)
15x = 300cm. (transport 15 to the right side )
x. = 300/15
x = 20cm
3 × 20 cm = 60cm
5 × 20 cm =100cm
7 × 20 cm = 140cm
(Thus the sides are 60 cm , 100 cm , 140 cm
Now ,
we have to find out the semi perimeter )
semi perimeter (s) = a+b+c
/2
= 60+100+140. 300
——————— = ——— = 150cm
2. 2
By using heron's formula
Area of a triangle= √s(s-a)(s-b)(s-c)cm
= √150(150-60)(150-100)(150-140)cm
=√150×90×50×10cm
= √3×5×10×3×3×10×10×5×10cm
= 1500√3cm²