the sides of a triangle are in the ratio of 17:15:8 of the perimeter of the triangle is 40 meter then the area of triangle is
Answers
The sides of a triangle are in ratio of 12:17:15 & the perimeter of the triangle is 540 cms. What is the area of the triangle?
Solution:
Start with simplest assumption with the side being a=12x cm, b=17x cm, 15 x cm; (as sides are in the ration 12:17:15)
Perimeter of triangle is given as 540 cm.
So, 12x + 17 x+ 15 x = 540
44 x = 540
x= 540/44 (=270/22 = 135/11)
Sides of triangle are : a=(12 * 135/11) cm; b= (17 * 135/11) cm ; c= (15 * 135/11) cm
Note: In the beginning you should always quickly check that it doesn’t belong to equilateral(1:1:1) neither forms a Pythagorean triplet so not a right angle triangle.
Now, since we know all the sides so we use the below formula to find the area of triangle.
Area=SQRT(s(s-a)(s-b)(s-c))
where s=(a+b+c)/2 or perimeter/2
S= 540/2 cm
S= 270 cm (=135*2)
Area=SQRT(270(270- 12*135/11)(270–17*135/11)(270–15*135/11))
Area =SQRT(135*2(135*2- 12*135/11)(135*2–17*135/11)(135*2–15*135/11))
Area =SQRT[ 135*2{(22- 12)/11}{(22–17)/11}{(22–15)/11} ]
Area = (135)^2 * SQRT[ 2*{(22- 12)/11}{(22–17)/11}{(22–15)/11} ]
Area = (135)^2 * SQRT[ 2*(10/11)*(5/11) *(7/11) ]
Area = (135)^2 * (10/11) * SQRT[ (7/11) ]
Area = (135)^2 * (10/11) * SQRT[ (7/11) ]
Area = (135)^2 * (10/11) * 0.797
Area = 13216.83 square cm
Explanation:
there sides of the triangle=17m,15m,8m
semi perimeter=40m/2=20m
area=√20(20-17)(20-15)(20-8)m²
=√2×2×5×3×2×5×2×3 m²
=2×2×3×5 m²
=60 m²