Question

If the sides of a triangle are $\text{39 cm, 80 cm, and 89 cm}$, then the triangle formed is a right-angled triangle.

• A. True
• B. False

Answer 1

The correct option is A

True

Pythagorean triple consists of three positive integers $\text{a, b, and c}$, such that $a^2+b^2=c^2$. Such a triplet is commonly written as $(a,b,c)$, and a well-known example is $(3,4,5)$. If $(a,b,c)$ is a pythagorean triplet, then so is $(ka,kb,kc)$ for any positive integer $k$. A primitive pythagorean triplet is one in which $a,bandc$ are coprime. A right triangle whose sides form a pythagorean triplet is called a pythagorean triangle.

The name is derived from the pythagorean theorem, stating that every right triangle has side lengths satisfying the formula $a^2+b^2=c^2$​. Thus, pythagorean triplets describe the three integer side lengths of a right triangle.

$(39,80,89)$ is a pythagorean triplet. So, the triangle formed will be a right angled triangle.

${39}^2+{80}^2={89}^2$
$1521+6400=7921$
$7921=7921$

Thus, $(39,80,89)$ is a pythagorean triplet.