Question

the sides of a right angle triangle contantaing the right angle are. (3 X) cm and (3 X +2) cm calculate the perimeter of triangle if the area of triangle is 24 cm²​

Answer 1

Answer:

Perimeter = 24 cm.

Step-by-step explanation:

Area = 1/2 * 3X ( 3X + 2)

  24  = 1/2 * ( 9X² + 6X)

  48  = 9X² + 6X

 (9X² + 6X - 48 = 0)/3

 3X² + 2X - 16 = 0

 3X² - 6X + 8X - 16 = 0

3(X - 2) + 8(X - 2) = 0

(X - 2) (3X +8) = 0

⇒ X = 2 or X = -8/3

Rejecting the negative value of x.

so x = 2

1st side = 3x = 3*2 = 6 cm

2nd side = 3x + 2 = 6 + 2 = 8 cm

So, by pythagorus theorem :-

3rd side = √(6²+ 8²)

so 3rd side = 10 cm

Perimeter = Sum of all sides

= 10 + 6 + 8

= 24 cm

Answer 2

Answer:

Area = (Base * Height) / 2

24 cm^2 = [3x * (3x + 2)] / 2  cm^2

9x^2 + 6x - 48 = 0

x = 2

Sides of triangle = 6cm, 8cm and sqrt(6^2 + 8^2)cm = 10 cm

Therefore perimeter = 6 cm + 8 cm + 10 cm = 34 cm