Question

the sides of right angle triangle are consecutive positive integer find the area of the triangle​

Answer 1

Answer:

The answer is 60 degrees for each angle.

Step-by-step explanation:

A interior angle of a triangle is a maximum and minimum of 180 degrees. Therefore, if the three consecutive angles are equal, then They each should be 60.

Answer 2

The sides of right angle triangle are consecutive positive integer. The area of right angled triangle is 6 square units  

Solution:

The sides of a right angled triangle are consecutive positive integers

Let the sides be x, x + 1, x + 2

Let the hypotenuse of triangle be (x + 2)

By Pythagoras theorem,

$hypotenuse^2 = opposite^2 + adjacent^2$

Therefore,

$(x+2)^2 = x^2 + (x+1)^2\\\\Expand\\\\x^2 + 4x + 4 = x^2 + x^2 + 2x + 1\\\\x^2 -2x -3=0\\\\Factor\\\\(x+1)(x-3) = 0\\\\Therefore\\\\x + 1 = 0\\\\x = -1\\\\x - 3 = 0\\\\x = 3$

We have,

x = -1 and x = 3

Given is a positive integer, so ignore -1

Therefore,

x = 3

x + 1 = 3 + 1 = 4

x + 2 = 3 + 2 = 5

Then the three sides of triangle are 3, 4 and 5

Base and height are 3 and 4 units respectively

$Area\ of\ triangle = \frac{1}{2} \times base \times height$

$Area\ of\ triangle = \frac{1}{2} \times 3 \times 4\\\\Area\ of\ triangle = 6$

Therefore the area of right angled triangle is 6 square units  

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