Question

Two sides of the equilateral triangle are reduced by $5$ cm and $4$ cm and third side of the triangle is increased by $4$ cm to form the right angled triangle. Find the original sides of equilateral triangle ?

• A. $25$ cm
• B. $26$ cm
• C. $1$ cm
• D. $29$ cm

Answer 1

The correct option is A $25$ cm

Let the original length of sides of equilateral triangle be $x$ cm.

Then, sides of right angled triangle will be $(x-4)$ cm,$(x-5)$ cm and $(x+4)$ cm.

By comparision, $(x+4)$ cm is the largest side, i.e., the hypotenous.


Now, applying Pythagoras theorem, we get
$(x+4{)}^2=(x-4{)}^2+(x-5{)}^2$
$\Rightarrow x^2+16+8x=x^2-8x+16+x^2-10x+25$

Rearranging the equation, we will have,
$x^2-26x+25=0$
The above equation can be expressed as,
$x^2-25x-x+25=0$
(taking $x$ common from the first two terms and $-1$ common from the last two terms)
$\Rightarrow x(x-25)-1(x-25)=0$
(taking $(x-25)$ common from both the terms)
$\Rightarrow (x-25)(x-1)=0$
$\Rightarrow x=25$ or $x=1$

But, if we take $x=1$ cm, the other two sides will be negative. So,$x=25$ cm is correct.

Hence, option $\left(a\right)$ correct.