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?

56

We know that,

H² = P² + B²

Area of right angled triangle = \(\frac{1}{2}\) × base × height

We have,

The difference between the two perpendicular sides of a right-angles triangle is 17 cm and its area is 84cm²

Let one side of triangle = a cm , other perpendicular side = a - 17 (Because difference between the two perpendicular sides of a right-angles triangle is 17 cm)

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 (∵ side cannot be negative)

Thus, H² = (24)² + (7)² = 625 = (25)²

3 sides of triangle are a = 24 cm, a - 17 = 7 cm and H = 25 cm

So,Perimeter of triangle = 24 + 7 + 25 = 56 cm