Question

Perimeter of right triangle is 30 cm and its area is 30cm2 .Find its sides​

Answer 1

Answer:

Sides of the right triangle are: 5cm, 12cm and 13cm

Step-by-step explanation:

Let the sides of the triangle forming the arms of the right-triangle be denoted as "b" and "h".

Let "x" be the hypotenuse (longest side).

ATQ,

Perimeter of Δ = 30cm

=> (b + h + x) = 30 ..........(i)

Area of Δ = 30 cm²

=> (1/2)*b*h = 30

=> b*h = 60  .........(ii)

Using Pythagoras theorem, we get:

b² + h² = x² ........(iii)

From (i)

(b + h + x) = 30

=> [(b+h) + x]² = 30²

=> (b+h)² + 2x(b+h) + x² = 900

=> b² + 2bh + h² + 2x(b+h) + x² = 900

=> (b² + h²) + 2bh + 2x(b+h) + x² = 900

Using (ii) and (iii)

=> x² + 2*60 + 2x(b+h) + x² = 900

=> 2x² + 120 + 2x(b+h) = 900

Using (i), we get: (b+h) = (30 - x)

=> 2x² + 120 + 2x(30 - x) = 900

=> 2x² + 120 + 60x - 2x² = 900

=> 60x = 780

=> x = 13

Hypotenuse of Δ = 13cm

Now we find the remaining sides:

Substituting for x in (i), we get:

(b + h) = 17      ...(iv)

Also, from (ii), we have:

bh = 60

=> b(17-b) = 60

=> 17b - b² = 60

=> b² - 17b - 60 = 0

=> b² - 12b -5b - 60 = 0

=> (b - 12)(b - 5) = 0

=> b = 12 or b = 5

Using (iv), we get:

If b = 12, then h = 5

If b = 5, then h = 12

Whichever option you choose, it means that two remaining sides are 12cm and 5cm.

The sides of Δ are: 5cm, 12cm and 13cm

Answer 2

Answer:

the correct answer is 5 cm,12 cm and 13 cm

Step-by-step explanation:

you can find answer in picture....

HOPE It HELPs !!♦️