Question

The perimeter of a triangle is 22 cm. If one of the sides is 9 cm, find the

other sides if the area of the triangle is 20.976 cm2 .

Answer 1

Explanation:

Perimeter of triangle is calculated by adding length of all three sides.

let side one be A= 9cm, another sides be respectively B and C.

hence A+B+C= 22 cm and B+C = 13, now AREA OF TRAINGLE = 20.976cm^2

Semi perimeter (s) = 22/2 = 11cm

as, area of triangle = square root (s * ( s-A) * (s-B) * (s-C))

20.976= square root (11* (11-9)*(11-B)*(11-C))

20.976*20.976= 11* (2) * (11-B) * (11-C)

439.99/22=121 -11C -11B +BC

19.99-121 = -11C -11B +BC

101= 11C + 11 B - BC

101 = 11*13 - BC

42= BC, now by substitution method, B=42/C, PUT this in perimeter equation hence 9+42/C + C=22

C=6, 7 and B= 42/C = 7,6respectively

Answer 2

• 6 cm and 7 cm

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