Question

The length of two sides of a right angled triangle containing the right angle differ by 2 cm. If the area of triangle is 24 cm, find the perimeter of triangle

Answer 1

Hola Friend ✋✋✋

Let one side be = x i.e base

then other side will be y i.e height

Their difference is 2

x - y = 2

y = x - 2.....

Area = ½ × b × h = 24

½ × x × ( x - 2 ) = 24

x² - 2x - 48 = 0

x² - 8x + 6x - 48 = 0

x × ( x - 8 ) + 6 × ( x - 8 ) = 0

( x + 6 ) × ( x - 8 ) = 0

x = - 6 or 8 cm

side cannot be in negative.... so x = 8 cm

y = x - 2 = 6 cm

Hypotenuse = √ ( 8² + 6² )

= √ ( 100 )

= 10 cm


So perimeter is.....

Perimeter = x + y + hypotenuse

= 8 + 6 + 10

= 24 cm......

Hope it helps

Answer 2

Answer:

Hello mate

Step-by-step explanation

Let the base of triangle be b cm and its height or perpendicular be p cm.

Given, p - b = 2 ... (1)

and area of triangle = 24 cm2

⇒

⇒

⇒

On putting the value of b in (1), we get

p - = 2

⇒ p2 - 2p -48 = 0

⇒ p2 - 8p + 6p -48 = 0

⇒ (p- 8) (p + 6) = 0

⇒ p = 8, -6

p ≠ -6. So, p = 8 cm

On putting p in (1), we get

⇒ b = 6 cm

So, Hypotenuse (h) =

Hence, perimeter of triangle = p + b + h = 8 cm + 6 cm + 10 cm = 24 cm

Hope it will help you