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STatiana [176]
3 years ago
12

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

Mathematics
2 answers:
wariber [46]3 years ago
7 0

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

maria [59]3 years ago
5 0

Answer:

12 cm, 5 cm,  13 cm

Step-by-step explanation:

<u>Sides of triangle:</u>

  • a, b, c

<u>Perimeter:</u>

  • P= a+b+c = 30

<u>Area:</u>

  • 1/2ab = 30 ⇒ ab = 60

<u>As per Pythagorean theorem, side c= √(a²+b²):</u>

  • 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

<u>Considering ab = 60</u>

  • 900+120=60a+60b ⇒ a+b = 17

<u>Again using ab= 60 to find out sides:</u>

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

<u>Solving the quadratic equation, its positive root is:</u>

  • a= 12

<u>Then we get the rest:</u>

  • b = 17 - 12= 5
  • c= 30 -17 = 13
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