Question

The sides of an equilateral triangle are shortened by 10unit,3units,2units respectively and the right triangle is formed. Then the length of each side of equilateral triangle is?

Answer 1

Step-by-step explanation:

Let the side of an equilateral A be= x units

new sides of new A=x-12; x-13; x-14. (x-12) side is the longest side in the right angled A

.ACCORDING TO THE PYTHAGORAS THEORAM

(x-13)? + (x-14)²= (X-12)?

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

2x2 + 365 - 54x = x2 + 144 -24x

2x2- x2 + 365 - 144 - 54x + 24x=0

x2 - 30x + 221 =0

x² -17x -13x + 221=0

x(x-17) -13(x-17)=0 (x-13)(x-17)=0

x-13=0 or x-17=0

x=13

x=17

*x #13 (because if x is 13 then side(x-13) of A would be zero which is impossible)

x= 17 units

side of the equilateral A is 17 units