Question

The hypotenuse of a right triangle is 5cm long the longer leg is 1cm longer than the shorter leg find the side lengths of the triangle

Answer 1

Answer:

Shorter leg=3

Longer leg=4

Step-by-step explanation:

Equations

In a right triangle, Pythagora's Theorem is satisfied. Being a the hypotenuse, b and c the legs of the triangle, then:

$a^2=b^2+c^2$

Let's call

x=the shorter leg of the triangle

The longer leg is 1 cm longer than the shorter leg, thus:

x+1=the longer leg.

Since the hypotenuse is 5 cm long:

$5^2=x^2+(x+1)^2$

Operating:

$25=x^2+x^2+2x+1$

Swapping sides and simplifying:

$2x^2+2x+1=25$

Subtracting 25:

$2x^2+2x-24=0$

Dividing by 2:

$x^2+x-12=0$

Factoring:

$(x-3)(x-4)=0$

We have two possible solutions:

x=3, x=4

The longer leg is x+1.

If x=3, x+1=4

If x=4, x+1=5. This solution is not valid because one leg would be equal to the hypotenuse.

Thus, the solution is:

Shorter leg=3

Longer leg=4