The perimeter of a triangle is 22cm. If one of the sides is 9cm, find the other sides if the area of the triangle is 20.976cm2

6 cm and 7 cm

Step-by-step explanation:

Given

A triangle with:

P = 22 cmA = 20.976 cm²a = 9 cmTo find Other sides of the triangleSolution

Let the missing sides be b and c

The perimeter is

P = a + b + c

Substitute known values

22 = 9 + b + cb + c = 13c = 13 - b

Use Heron's formula for the area:

A = √s(s-a)(s-b)s-c), where s is half-perimeters = 22/2 = 11

Substitute s, a and c and solve for b:

√11(11 - 9)(11 - b)(11 - c) = 20.976√11*2(11 - b) (11 - 13 + b) = 20.976√22(11 - b)(b - 2) = 20.976

Square both sides

22(11 - b)(b - 2) = 20.976²22(11 - b)(b - 2) ≈ 440(11 - b)(b - 2) = 20 13b - b² - 22 = 20b² - 13b + 42 = 0b = (13 ± √13² - 4(42))/2b = (13± 1)/2b = 6, b = 7

Find c:

c = 13 - bc = 6, c = 7

So missing sides are 6 cm and 7 cm

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