Question

find the value of x(7,x,x+1) is a Pythagorean triplet.​

Answer 1

$\large\text{\underline{Required}}$

The value of $x$ such that $(7,x,x+1)$ is a Pythagorean triplet.

$\large\text{\underline{Note}}$

$\large\red{\bigstar}\text{Pythagorean triple}$

The Pythagorean triple is three side lengths of a right triangle. Also, the number is in ascending order.

$\large\red{\bigstar}\text{Triangle inequality}$

When there is the longest length and the remaining two sides, the sum of two shorter sides is always greater than the longest side.

$\large\text{\underline{Solution}}$

The length of three segments of a right triangle is called a Pythagorean triplet. This means the Pythagorean theorem must satisfy.

However, the longest side must satisfy triangle inequality.

$\implies x+1<x+7$

As this is obvious, we will not consider this inequality.

The equation which must satisfy the Pythagorean theorem is the following.

$\implies7^{2}+x^{2}=(x+1)^{2}$

$\implies49+x^{2}=x^{2}+2x+1$

$\implies 2x+1=49$

$\implies 2x=48$

$\implies x=24$

$\large\text{\underline{Conclusion}}$

The value of $x$ is $24$.

$\large\text{\underline{Verification}}$

Pythagorean triple: $(7,x,x+1)$ where $x=24$.

$\implies 7^{2}+x^{2}=(x+1)^{2}\text{ where }x=24$

$\implies 7^{2}+24^{2}=25^{2}$

$\implies 49+576=625$

$\implies625=625$

The lengths of the triangle satisfy the equation. Hence, it is verified that the triangle is a right triangle.

Answer 2

Step-by-step explanation:

• Applying the Pythagorean triples rule as

• a² + b² = c²

• 5² + x² = 13²

• 25 + x² = 169

• x² = 169-25

• x² = 144