The triangle with sides of lengths 48mm, 5cm, and 1.4cm is a right-angled triangle.
How do we determine a right-angled triangle?
A right-angled triangle is a triangle with one right angle, that is the value of one angle is 90°. The other two angles are acute angles, which are less than 90°.
How do we determine the sides of a right-angled triangle?
The side opposite the right angle, that is, the side opposite 90°, is the largest side of the triangle and is called the hypotenuse.
What is the Pythagoras Theorem?
According to the Pythagoras theorem, the square of the hypotenuse is the sum of the squares of the other two sides. If we say the hypotenuse is 'c' and the other two sides are 'a' and 'b', then by the theorem:
a² + b² = c².
How do we solve the given question?
We are asked to check whether the triangles with the side 48mm, 5cm, and 1.4cm is a right-angled triangle.
We will use the Pythagoras theorem to check whether the triangle is right-angled or not.
We first make the units of the side the same.
We know:
10mm = 1cm
or, 1mm = 0.1cm.
We will convert 48mm to cm,
48mm = 48*0.1cm = 4.8cm.
Now we have our three sides as 4.8cm, 5cm, and 1.4cm.
The longest side will be taken as the hypotenuse, that is, we will take 5cm as the hypotenuse.
By Pythagoras' Theorem,
the square of hypotenuse = the sum of squares of other sides
or, 5² = 4.8² + 1.4²
or, 25 = 23.04 + 1.96
or, 25 = 25.
This is true, so Pythagoras' theorem stands.
∴ The triangle with sides of lengths 48mm, 5cm, and 1.4cm is a right-angled triangle.
Learn more about Pythagoras' Theorem and the right-angled triangle at
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