Question

The length of hypotenuse of a right angled triangle is 15 cm and its area is 54 cm2

. Find the length of the

perpendicular sides.​

Answer 1

Answer:

Step-by-step explanation:

Let b be the base and h be the height of the perpendicular sides.

By Pythagoras Theorem,

b² + h² = 15²

=> b² + h² = 225  ----- (1)

Area of right angled triangle = 1/2 * b * h = 54 cm²

=> bh = 108 ----- (2)

//Two ways to find out value of b and h:

1. Pythagorean triplet

we can see  that 12, 9,15 is the Pythagorean triplet which will satisfy both (1) and (2).

thus b = 12 cm an h = 9 cm.

2.

//We know that (a +b)² = a² + b² + 2ab

(b + h)² = b² + h² + 2bh

           = 225 + 216 = 441

   => b + h = 21        ---------------- (3)

(b - h)² = b² + h² - 2bh

           = 225 - 216 = 9

 => b - h = 3        ---------------- (4)

Solving (3) and (4) by addition,

b + h = 21

b - h = 3

---------------

2b = 24

=> b = 12

=> h = 9.

Thus the lengths of perpendicular sides are 12 cm  and 9 cm.