Question

4. If the difference between the sides angled triangle is 3 cm and its area is find its perimeter.​

Answer 1

Correct Question:

If the difference between the sides of a right angled triangle is 3 cm and its area is 54 cm². Find its perimeter.

Answer:

• Perimeter of right angled triangle is 36 cm.

Step-by-step explanation:

Given:

• Area of right angled triangle = 54 cm²
• Difference between sides = 3 cm

To Find:

• Perimeter of triangle.

Now, let two sides of triangle be, 'x' and 'x + 3'.

⇒ Area of triangle = 1/2 × base × height

⇒ 54 = 1/2 × (x) × (x + 3)

⇒ 54 = 1/2 × x² + 3x

⇒ 108 = x² + 3x

⇒ x² + 3x - 108 = 0

⇒ x² + 12x - 9x - 108 = 0

⇒ x(x + 12) - 9(x + 12) = 0

⇒ (x - 9)(x + 12) = 0

⇒ x = 9 and - 12

But we know that sides cannot be negative,

So, sides are 9 cm and 12 cm.

Now, we will calculate 3rd side by Pythagoras theorem,

⇒ A² = B² + C²

⇒ A² = 9² + 12²

⇒ A² = 81 + 144

⇒ A² = 225

⇒ A = 15 cm

Now, we will calculate perimeter,

⇒ Perimeter of triangle = A + B + C

⇒ Perimeter of triangle = 15 + 9 + 12

⇒ Perimeter of triangle = 36 cm.

Hence, Perimeter of right angled triangle is 36 cm.

Answer 2

Let the two sides be x and x + 3

Area = 54 cm^2

1/2 (x)(x+3) = 54

x² + 3x = 108

x² + 3x - 108 = 0

(x+12)(x-9) = 0

x = 9

Sides are 9 cm and 12 cm

Hypotenuse = root of 9^2 + root of 12^2

= root of 225 = 15cm.

Perimeter of triangle = A + B + C

= 15+9+12 = 36cm