Question

The perimeter if a right angle triangle is 12cm a d it's hypotenus between other two sides is 4cm. Find it's area by Heron's formula.
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Answer 1

Step-by-step explanation:

Given perimeter of the right angle triangle = 12cm

hypotenuse of the triangle = 5cm

let the all three sides of the right angle triangle be a, b and c respectively. where c is the hypotenuse of the right angle triangle.

we know that,

perimeter of a triangle = sum of all three sides

⇒ a + b + c = 12cm

⇒ a + b + 5 = 12cm

⇒ a + b = 12 - 5

⇒ a = 7 - b ------(i)

by pythegoras theorem, we get

⇒ c² = a² + b² ------(i)

substituting value of a from equation (i) in equation (ii)

⇒ 5² =  (7 - b)² + b²

⇒ 25 = (7)² - 2(7)(b) + (b)² + b²

⇒ 25 = 49 - 14b + 2b²

⇒ 2b² - 14b + 24 = 0

taking 2 as common,

⇒ b² - 7b + 12 = 0

by factorization, we get

⇒ b² - (4b + 3b) + 12 = 0

⇒ b² - 4b - 3b + 12 = 0

⇒ b(b - 4) - 3(b - 4) = 0

⇒ (b - 4) (b - 3)

∴ b = 4 or 3

if b = 4, then a = 7 - 4 = 3

if b = 3, then a = 7 - 3 = 4

so, we can say the the other two sides of the right angle triangle (base and perpendicular) are 3cm and 4cm respectively.

∴ area of the right angle triangle = 1/2 * b * h

= 1/2 * 3 * 4

= 3 * 2

= 6cm²