Question

The perpendicular of a right angled triangle is 9cm and three sides are in ap. Find the integral value of the length of the hypotenuse.

Answer 1

Answer:11.25cm

Step-by-step explanation:

Let the difference between them be x

Hypotenuse is the largest side so take it 9+x

Take base 9-x

9²+(9-x)²=(9+x)²

9²+9²+x²-18x=9²+x²+18x

9²=36x

81=36x

x=2.25

9+x=11.25cm

Answer 2

Answer:

Hypotenuse=27 cm

Step-by-step explanation:

The three sides of the given right angled triangle are in A.P.

Let the perpendicular be a=9 cm

∴Base = a+d , where d is common difference.

Base=9+d

Hypotenuse =a + 2d = 9 + 2d  -----eq1

By Pythagoras Theorem

9² + (9+d)² = (9+2d)²

81 + 81+d²+18d = 81+4d²+36d

3d²+18d-81 = 0

d²+6d-27 = 0

d²+9d-3d-27 = 0

d(d-9)+3(d-9) = 0

(d-9)(d+3) = 0

d=9   d=-3

∵ d cannot be negative, d=9

From eq1, Hypotenuse = a+2d

=9+2×9

=9+18

=27 cm