The difference between the two perpendicular sides of a right-angled triangle is 2 cm and its area is 24 cm2 . What is the perimeter (in cm) of the triangle?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 24.
Let one side of the given triangle be x.
⇒ The other side = x + 2
Given that, area of triangle = 24 cm
Area of right angled triangle = ½ × base × height
⇒ 24 = ½ × (x + 2) × x
⇒ x2 + 2x - 48 = 0
⇒ x2 + 8x - 6x - 48 = 0
⇒ x(x + 8) - 6(x + 8) = 0
⇒ (x - 6)(x + 8) = 0
⇒ x = 6; x = -8 (not possible)
So, x = 6 cm; (x + 2) = 8 cm
Applying the Pythagoras theorem,
H2 = 36 + 64
⇒ H2 = 100
⇒ H = 10 cm
Perimeter of triangle = 6 + 8 + 10 = 24 cm
Hence the perimeter (in cm) of the triangle is 24.