Question

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

Answer 1

Let the side of an equilateral Δ be= x units
-----------------------------------------------------
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
--------------------------------------------------------------
side of the equlateral Δ is 17 units

Answer 2

Let the side of an equilateral Δ be= x units

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

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 impossible)

∵x= 17 units

side of the equilateral Δ is 17 units