Question

The lengths of two sides of a right triangle containing the right angle differ by 2 cm. If the area of the triangle is 24cm² . Find the perimeter of the triangle​

Answer 1

Answer:

Given :

• The lengths of two sides of a right triangle containing the right angle differ by 2 cm.

• If the area of the triangle is 24cm² .

To Find :

• Find the perimeter of the triangle

Solution :

Let, two sides of right-angle triangle containing the right angle be x  cm and x + 2  cm,

According to the Question :

→ Area of triangle = 24 cm²

Substitute all values :

→ 1/2 × ( x ) × ( x + 2 ) = 24

→ 1/2 × ( x² + 2 x ) = 24

→ x² + 2 x - 48 = 0

→ x² + 8 x - 6 x - 48 = 0

→ ( x - 6 ) ( x + 8 ) = 0

→ x = 6   or  x = - 8

• since, length can't be negative therefore,

sides of triangle would be [ x = 6 cm ] and [ x + 2 = 8 cm ]

According to the Pythagoras theory

→ hypotenuse² = length² + base²

Substitute all values :

→ hypotenuse² = ( 6 )² + ( 8 )²

→ hypotenuse² = 100

→ hypotenuse = 10 cm

Now,

calculating perimeter of triangle

→ Perimeter of triangle = 6 cm + 8 cm + 10 cm

→ Perimeter of traingle = 24 cm

Therefore,

• Perimeter of triangle will be 24 cm.

Answer 2

Answer:

Let x cm be the one of the sides, then (x 2)cm be another side.

Area of triangle = 24 cm² (given)

We know, Area of triangle 2 (Base x

height)

1 2 24 xxx (x - 2)

→ 48 = x? 2x

or x? – 2x – 48 = 0

Solving above equation, we have

(x + 6)(x 8) = 0 -

x= -6 or x = 8

Since length measure cannot be negative,

so neglect x = -6

One side = 8 cm

Another Side = x - 2 = 8 - 2 = 6 cm

Apply Pythagoras theorem:

Hypotenuse? = Base? + Perpendicular?

Hypotenuse? = V(82 + 6?) =

Hypotenuse = V100 10

Therefore, perimeter of triangle = Sum of all

the sides = (6+ 8 + 10)cm = 24 cm