Question

Find the area of a triangle , two sides of which are 17cm and 10 cm and perimeter is 48 cm.​

Answer 1

Answer:

let a b c be the sides of the given triangle and 2s be its perimeter such that a=17cm b=10cm and 2s =48cm

now a+b+c=2s

17+10+c=48

c=21

s=a+b+c/2

s=24 cm

s-a=24 -17=7

s-b=24-10=14

s-c=24-21=3

area of given triangle = root s(s-a)(s-b)(s-c)

root 24×7×14×3=root 2×2×2×3×7×7×2×3

2×2×3×7=84cm^2

Answer 2

1) Let the length of 3rd side of the Triangle be x.

2) Perimeter of a Triangle = Sum of all it's sides.

3) Therefore, 48 = 17 + 10 + x

x = 21

4) Using Heron's Formula to find the Area of Triangle using it's Perimeter. i.e. - s√[(s - a)(s - b)(s - c)]. Here s = p/2 or 48/2 = 24

5) 24√[(24 - 17)(24 - 10)(24 - 21)]

6) Your Answer ≈ 411.51