SOLUTION
Given the question in the question tab, the following are the solution steps to answer the question.
STEP 1: Define a right-angled triangle
A right triangle or right-angled triangle, or more formally an orthogonal triangle, is a triangle in which one angle is a right angle.
STEP 2: Define the sides of a right-angled triangle
There are three sides for a right angled triangle which are the hypotenuse, adjacent and the opposite. In geometry, a hypotenuse is the longest side of a right-angled triangle, the side opposite the right angle. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides.
[tex]\begin{gathered} \text{By Pythagoras theorem,} \\ \text{Hypotenuse}^2=opposite^2+adjacent^2 \end{gathered}[/tex]STEP 3: Get a uniform unit for the given sides of the triangle
[tex]\begin{gathered} \text{sides are }48\operatorname{mm},5\operatorname{cm},1.4\operatorname{cm} \\ \text{To have uniform unit for the sides, we convert the sides in mm to cm} \\ 1\operatorname{cm}=10\operatorname{mm} \\ \text{xcm}=48\operatorname{mm} \\ By\text{ cross multiplication,} \\ 10x=48 \\ \text{Divide both sides by 10} \\ \frac{10x}{10}=\frac{48}{10} \\ x=4.8\operatorname{cm} \\ \\ \text{The new sides of the triangle becomes 4.8cm,5cm and 1.4cm} \end{gathered}[/tex]STEP 4: Determine if the triangle is a right-angled triangle
[tex]\begin{gathered} For\text{ a right-angled triangle, the longest side is the hypotenuse and } \\ \text{Hypotenuse}^2=opposite^2+adjacent^2 \\ \text{The longest side will be 5cm while the other sides will be 1.4cm and 4.2cm} \\ By\text{ pythagoras theorem,} \\ 5^2=4.8^2+1.4^2 \\ 5^2=23.04+1.96 \\ 25=25 \end{gathered}[/tex]Since it can be seen the square of the biggest side(hypotenuse) is equal to the sum of square of the other two sides, i.e, it follows pythagoras theorem, hence, the triangle is a right-angled triangle.
