Question

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

Answer 1

Let one side containing the right angle=x Other side containing right angle would be=x+2 1/2*base*height=area of triangle 1/2*x*x+2=24 x^2+2x/2=24 x^2+2x=24*2=48 x^2+2x-48=0 By factorisation x^2+[8-6]x+8*-6 Therefore the sides are 8,6 By pythagorus theorem The third side will be 10 Perimeter of triangle =8+6+10=24.

Answer 2

Answer:

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 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.