The difference between the two perpendicular sides of a right-angled triangle is 17 cm and its area is 84 cm2. What is the perimeter (in cm) of the triangle?
Answer & explanation
Correct answer: option 4
Let one side of triangle = a cm
Other perpendicular side = a - 17
Area of right angled triangle = \(\frac{1}{2}\) × a × (17 - a) = 84
= a2 – 17a - 168 = 0
= a2 – 24a + 7a - 168 = 0
= a(a - 24) +7 (a - 24) = 0
= (a +7) (a - 24) = 0
= a = 24
Thus, H2 = (24)2 + (7)2 = 625
H = 25
Sides of triangle are a = 24 cm,
a - 17 = 7 cm
H = 25 cm
Perimeter of triangle = 24 + 7 + 25 = 56 cm