Practicing Success
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? |
40 49 36 56 |
56 |
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 |