Question

9. 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 24 cm", find the perimeter of the triangle. ​

Answer 1

Answer:

24 cm

Step-by-step explanation:

let side₁ be x

and side₂ be y  where x > y

and given that y = x - 2

Also area of triangle = (side1 x side 2) / 2

also given already that

area of the right triangle = 24 cm

=>   24 =  (side1 x side 2) / 2

=>  24 =  (x)(x-2) / 2

=>  24 X 2 = x² - 2x

=>  48 = x² - 2x

=>  x² - 2x - 48 = 0

Now solving the quadratic equation using the middle term splitting or quadratic  formula, we get

x² - 8x + 6x - 48 = 0

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

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

therefore the value of x is 8 or -6

-6 is neglected as the length of a side can never be negative.

therefore, x = 8

So y = 8 - 2

    y = 6

now using the Pythagoras theorem we get the hypotenuse

H² = A² + B²

H² = 8² + 6²

H² = 64 + 36

H² = √100

H = 10 cm

Now, perimeter =  S₁ + S₂ + S₃

                          = 8 + 6 + 10

                          = 24 cm