Question

The two sides of a right-angled triangle equal and the square of its hypotenuse is 50cm square. Find the length of the each find the length of each side.​

Answer 1

Answer:

Let the two sides of given Triangle be x,x

Square of hypotenuse is 50cm

2

From Pythagorous theorm

c

2

=a

2

+b

2

50=x

2

+x

2

2x

2

=50

x

2

=25

x=

25

x=5

So the length of each side is 5cm

Answer 2

$\huge\color{pink}{\textbf{\textsf{Required \: Answer}}}$

$\Longrightarrow$ 5cm

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$\underline{\sf{\green{EXPLAINATION:-}}}$

★ Given,

length of two equal sides of a triangle is equal to the hypotenuse which measures 50cm².

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★ Find:-

• Length of the each side.

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★ Therefore,

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By Pythagoras theorem,

$\begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{{ {H}^{2} = {a}^{2} + {b}^{2} }\:}}\end{gathered}$

$\: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{{ {50}^{2} = {x}^{2} + {x}^{2} }\:}}\end{gathered}$

$\: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\;\;\bf{{ {50} = {2x}^{2}}\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\; {x}^{2} = \;\bf{{ \frac{50}{2} = 25 }\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\; {x} = \;\bf{{ \sqrt{25}}\:}}\end{gathered}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \begin{gathered}\\\;\sf{:\rightarrow\;\; {x} = \;\bf{{{5}}\:}}\end{gathered}$

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∴ The length of other two equal sides would be 5cm each.

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$\underline{\sf{\green{Information \: Related \: to \: Pythagoras:-}}}$

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•A right angled triangle has one of its angles equals to 90°.

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•The side opposite to the right angle is called the Hypotenuse.

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•The other two sides that contain right angle are called the base and perpendicular of the right angled triangle.

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• The two sides of a right triangle other than the Hypotenuse are called its legs.

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• Formula :- H² = B² + P²

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★ A relationship between hypotenuse, base and perpendicular of a right angled triangle was given by Greek Mathematician Pythagoras, who was born in 570 B.C.