The difference between the two perpendicular sides of a right-angled triangle is 17 cm and is 84 cm2. What is the perimeter (in cm) of the triangle?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 56
Let one side of the triangle = x cm
Another perpendicular side = x - 17 (the difference between the two perpendicular sides of a right-angles triangle is 17 cm)
Area of right angled triangle = 1/2 × x × (17 - x) = 84
x2 - 17x -168 = 0
⇒ x2 - 24x + 7x - 168 = 0
⇒ x(x - 24) + 7(x - 24) = 0
⇒ (x + 7)(x - 24) = 0
⇒ x = 24 (side cannot be negative)
Thus, H2 = (24)2 + (7)2 = 625 = (25)2
3 sides of triangle are x = 24 cm, x - 17 = 7 cm and H = 25 cm
Therefore, Perimeter of triangle = 24 + 7 + 25 = 56 cm