Question

the sides of an equilateral triangle are shortened by 12 units,13units,14units respectively and a right angle triangle is formed.find the length of each side of the equilateral triangle

Answer 1

Answer:The side of the equilateral triangle is. 17 units.

Step-by-step explanation:

New sides of new Δ=x-12; x-13; x-14.

(x-12) side is the longest side in the right angled Δ

ACCORDING TO THE PYTHAGORAS THEORAM

(x-13)² + (x-14)²= (X-12)²

after opening the brackets...

x² + 169 - 26x + x² + 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 Δ would be zero

                                which is imposiible)

x= 17 units