Question

The perimeter of a right angled triangle is 30cm and its area is 30cm square then find the side of triangle

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Answer 1

12 cm, 5 cm, 13 cm

Explanation:

Sides of triangle:

• a, b, c

Perimeter:

• P= a+b+c = 30

Area:

• 1/2ab = 30 ⇒ ab = 60

As per Pythagorean theorem, side c= √(a²+b²):

• a+b+c = 30
• a+b+ √(a²+b²) = 30
• a+b - 30= - √(a²+b²)
• (a+b - 30)²= (- √(a²+b²))²
• a²+b²+900 + 2ab - 60a - 60b = a²+b²

Considering ab = 60

• 900+120=60a+60b ⇒ a+b = 17

Again using ab= 60 to find out sides:

• ab=60
• a(17-a)= 60
• 17a - a² -60 = 0
• a² -17 a +60= 0

Solving the quadratic equation, its positive root is:

• a= 12

Then we get the rest:

• b = 17 - 12= 5
• c= 30 -17 = 13

Answer 2

Perimeter = a + b + c = 30

Area = 1/2 x a x b = 30

Multiples of 30: 2, 3, 5, 6, 10, 12, 15

For perimeter c = 30- (a+b)

C= sqrt( a^2 + b^2)

Using the possible combinations of the above:

5 and 12:

C = sqrt(5^2 + 12^2) = 13

5 + 12 + 13 = 30 for the perimeter

Area = 1/2 x 5 x 12 = 30

The sides are 5, 12 and 13 cm