Question

is it possible to design a right triangle in which the hypotenuse is 26 cm and the difference between the lengths of the other two sides is 14 cm? if so, find the length of these sides.

Answer 1

Given

Right triangle in which the hypotenuse is 26 cm and the difference between the lengths of the other two sides is 14 cm.

To find

The lengths of the sides of the triangle other than the hypotenuse

Solution

Let us find the sides of the triangle to know if such a design is actually possible.

Let the sides of the triangle be x and y

$x-y=14\\\Rightarrow x=y+14$

From Pythagoras theorem we get

$x^2+y^2=26^2\\\Rightarrow (y+14)^2+y^2=676\\\Rightarrow y^2+196+28y+y^2=676\\\Rightarrow 2y^2+28y-480=0\\\Rightarrow y^2+14y-240=0$

Solving the quadratic equation

$y=\dfrac{-14\pm \sqrt{14^2-4\cdot 1\left(-240\right)}}{2\cdot 1}\\\Rightarrow y=10,-24$

So, $y=10$ and $x=y+14=10+14=24$

The design of the triangle mentioned is possible.

The other two sides of the triangle are 10 cm and 24 cm.