Question

the sides of an equilateral triangle are shortened by 12 units 13 units and 15 units respectively and a right angle triangle is formed. The side of the equilateral triangle is?​

Answer 1

Answer:

The answere is given to the picture

Answer 2

⇒SOLUTION:-

Let 'x' be the length of each side of the equilateral triangle. 

Then, the sides of the right angle triangle are

(x - 12), (x - 13) and (x - 14) 

In the above three sides, the side represented by (x - 12) is hypotenuse (Because that is the longest side). 

Using Pythagorean theorem, we have:-

⇢(x - 12)²  =  (x - 13)² + (x - 14)²

⇢ x² - 24x + 144  =  x² - 26x + 169 + x² - 28x + 196

⇢x² - 30x + 221  =  0 

⇢(x - 13)(x - 17)  =  0 

⇢x  =  13  or  x  =  17. 

x=13 can not be accepted.

Because, if x=13, the side represented by (x - 14) will be negative. 

So, the side of the equilateral triangle is 17 units.