Question

Two sides of an equilateral triangle are reduced by 5 units and 4 units, respectively, and the third side of the triangle is increased by 4 units to form a right-angled triangle. Find the length of the original side of the equilateral triangle.

• A. 24 units
• B. 1 units
• C. 25 units
• D. 29 units

Answer 1

The correct option is C 25 units

Let the original length of sides of an equilateral triangle be x units.

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

By comparison, (x + 4) unit is the largest side, i.e., the hypotenuse.


Now, applying Pythagoras theorem, we get:
$(x+4{)}^2=(x-4{)}^2+(x-5{)}^2$

$x^2+16+8x=x^2-8x+16+x^2-10x+25$

Rearranging the equation:
$x^2-26x+25=0$

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}
$\Rightarrow (x-25)(x-1)=0$

$\Rightarrow x=25\text{or}x=1$

But, if we take x = 1, the other two sides of the equilateral will be negative.

So, x = 25 is correct.

∴ Each side of the equilateral triangle is 25 units.

Hence, option (a) is correct.