Question

the lengths of the two sides of a right triangle containing the right angle differ by 2 cm. if the area of the triangle is 24cm^2, find the perimeter of the triangle.​

Answer 1

Step-by-step explanation:

• Area of triangle = 24 cm²

• Let the height of the right angle triangle be x cm and base be y cm.

It is given that, the lengths of the two sides of a right triangle containing the right angle differ by 2 cm :]

Therefore,

➳ x - y = 2 cm

➳ x = 2 + y .........[Equation (i)]

• As it is said in question that we need to find the area of triangle. So, to Calculate area of triangle we have to use below given formula :]

➳ Area of Triangle = ½ × base × height

• Now,using this formula we will calculate the area of triangle :]

➳ 24 = ½ * y * (2 + y)

➳ 48 = 2y + y²

➳ y² + 2y - 48 = 0

➳ y² + 8y - 6y - 48 = 0

➳ y(y + 8) - 6(y + 8) = 0

➳ (y + 8) (y - 6) = 0

➳ y = -8 or 6

• Side of the triangle cannot be negative. Therefore, y = 6 cm

Now, Putting the value y = 6 in equation (i) we get,

➳ x = 2 + y

➳ x = 2 + 6

➳ x = 8 cm

Therefore,

• Base of triangle = y = 6 cm

• Height of the triangle = x = 8 cm

Now, we will find the third side of a right angle triangle by using the Pythagoras theorem.

➳ (Hypotenuse)² = (Oneside)² + (Other side)²

➳ Hypotenuse² = 8² + 6²

➳ Hypotenuse² = 64 + 36

➳ Hypotenuse² = 100

➳ Hypotenuse = 10 cm

Hence, the third side of a Triangle is 10 cm.

Now, we can calculate the perimeter of triangle :

➳ Perimeter of triangle = 8 + 6 + 10

➳ Perimeter of triangle = 24 cm

Therefore, the perimeter of triangle is 24 cm.

Answer 2

Answer:

• Perimeter of triangle = 24 cm

Explanation:

Given that,

• Lengths of the two sides of a right-angle triangle containing the right angle differ by 2 cm
• Area of the triangle is 24 cm²

To find,

• Perimeter of triangle =?

Solution,

Let, two sides of right-angle triangle containing the right angle be x  cm and x + 2  cm, then these sides will be the base and height of right triangle.

so,

→ Area of triangle = 24 cm²

→ 1/2 . ( x ) . ( x + 2 ) = 24

→ 1/2 . ( x² + 2 x ) = 24

→ x² + 2 x = 48

→ x² + 2 x - 48 = 0

splitting the middle term

→ x² + 8 x - 6 x - 48 = 0

→ x ( x + 8 ) - 6 ( x + 8 ) = 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 ]

Now, using Pythagoras theorem in right triangle

→ hypotenuse² = length² + base²

→ hypotenuse² = ( 6 )² + ( 8 )²

→ hypotenuse² = 36 + 64

→ 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.