Question

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​

Answer 1

Answer:

• 6 cm and 7 cm

Step-by-step explanation:

Given

A triangle with:

• P = 22 cm
• A = 20.976 cm²
• a = 9 cm

To find

• Other sides of the triangle

Solution

Let the missing sides be b and c

The perimeter is

• P = a + b + c

Substitute known values

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

Use Heron's formula for the area:

• A = √s(s-a)(s-b)s-c), where s is half-perimeter
• s = 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) = 20.976²
• 22(11 - b)(b - 2) ≈ 440
• (11 - b)(b - 2) = 20
• 13b - b² - 22 = 20
• b² - 13b + 42 = 0
• b = (13 ± √13² - 4(42))/2
• b = (13± 1)/2
• b = 6, b = 7

Find c:

• c = 13 - b
• c = 6, c = 7

So missing sides are 6 cm and 7 cm