Question

If in a right angle triangle the sides of its base is 5 and the other side is 12 then its hypotenuse is 13.

True OR False​

Answer 1

Given :

• Base of a right angled triangle = 5cm
• Other side of a right angled triangle = 12cm
• Hypotenuse of a right angled triangle = 13cm

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To do :

• We need to verify if the hypotenuse of the said right angled triangle measures 13cm or not.

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How do we proceed ?

➻ For a right angled triangle we use Pythagoras theorem which follows as ,

⠀⠀⠀⠀The Pythagoras theorem also known as Pythagorean theorem, states that the sum of the squares of the two sides of a triangle equals to the square of the longest side (hypotenuse) of the triangle.

Or, The square of the hypotenuse of a right angled triangle equals to the sum of the squares of base and perpendicular of the triangle.

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Solution :

According to Pythagoras theorem,

$\sf\:(Hypotenuse)^{2}~=~(Base)^{2}+(Perpendicular)^{2}$

$\sf\:\to\:(13)^{2}=(5)^{2}+(12)^{2}$

$\sf\:\to\:169=25+144$

$\sf\:\to\:169=169$

Hence Verified!~

$\sf\:\star$ $\bf\:Therefore~, the~given~sentence~is~True.$

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⠀⠀⠀⠀For a right angled triangle having base as 5cm and other side (perpendicular) as 12cm hypotenuse will be 13cm.

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Answer 2

True. If in a right angle triangle the sides of its base are 5 and the other side is 12 then its hypotenuse is 13.

• If a triangle is a right-angled triangle then one of its angles must be 90 degrees and the side opposite to the 9o degrees is said to be the hypotenuse.
• To get a relation between the three sides of the triangle Pythagoras derived a relation that is square of the hypotenuse is equal to the sum of squares of the base and altitude,
• In this case if the hypotenuse is 13 and the other two sides are 5 and 12 then the same can be said for this situation,
• $13^2=5^2+12^2\\169=169$Hence, it is true.