Question

The Hypotenuse of a right triangle is 0.5 units long. The longer leg is 0.1 units longer than the shorter leg. Find the lengths of the sides of the triangle.​

Answer 1

Answer:

The lengths of the sides of a right triangle are

Longer leg = 0.4 units.

Shorter leg = 0.3 units.

Step-by-step explanation:

Given:

Hypotenuse = 0.5 units

Let the length of shorter leg of right triangle be x units then

According to the given condition,

length of longer leg will be (0.1 + x) units

Now,we know for a right triangle,by Pythagoras theorem we have

$(\textrm{Hypotenuse})^{2} = (\textrm{Longer leg})^{2}+(\textrm{Shorter leg})^{2}$

substituting the values we get

$0.5^{2}= (x+0.1)^{2}+ x^{2}$

Applying $(a+b)^{2}= a^{2}+2ab+b^{2}$  we get

$0.25= x^{2} +2\times 0.1\times x+ 0.1^{2} + x^{2} \\2x^{2} +0.2x+0.01-0.25=0\\2x^{2} +0.2x-0.24=0$

which is a quadratic equation

dividing the equation throughout by two we get

$x^{2} +0.1x-0.12=0\\\textrm{on factorizing we get}\\x^{2} +0.4x-0.3x-0.12=0\\(x+0.4)(x-0.3)=0$

$\therefore (x-0.3)= 0\\\therefore x=0.3$

Since x cannot be negative we  take

x = 0.3 units

∴ Longer leg = x + 0.1

                     = 0.3+0.1

                     =0.4 units

So, the lengths of the sides of a right triangle are

Longer leg = 0.4 units.

Shorter leg = 0.3 units.