Question

If c is the hypotenuse of a right triangle , of sides a , b and c , find the third side.
a) a = 9 cm and c = 41 cm

Answer 1

Answer:

40cm

Step-by-step explanation:

According to Pythagoras theorem

a square + b square equals to c square

9 square + b square = 41 square

81+ b square=1681

b square=1600

b =40cm

May be helpful

Answer 2

Correct Question :

• If AC is the hypotenuse of a right triangle ABC then find the third side.

Given :

• AB → 9 cm
• AC → 41 cm

Now,

As we know , that the given triangle is right angled so we can apply Pythagoras Theorem in it. So, we have two sides with measures 9 cm and 41 cm respectively. Out of which AC is hypotenuse.

Now, let's solve it :

According to the Pythagoras Theorem , the sum of the square of Base side and perpendicular side is equal to the square of the longest side i.e, hypotenuse.

Pythagoras Theorem :

⠀⠀⠀⠀⠀⠀${\bullet \: {\boxed{\sf {AC^{2} = AB^{2} + BC^{2}}}}}$

Considering the unknown side be ' x ' cm.

Then ,

• AB → 9 cm
• BC → x cm
• AC → 41 cm

Putting up the respective values , we get :

$\dashrightarrow\:\:\sf AC^{2} = AB^{2} + BC^{2}$

$\dashrightarrow\:\:\sf 41^{2} = 9^{2} + x^{2}$

$\dashrightarrow\:\:\sf 1681 = 81 + x^{2}$

$\dashrightarrow\:\:\sf 1681 - 81 = x^{2}$

$\dashrightarrow\:\:\sf 1600 = x^{2}$

$\dashrightarrow\:\:\sf x = \sqrt 1600$

$\dashrightarrow\:\:\sf x = 40$

$\dashrightarrow\:\: \underline{ \boxed{\sf Third \: side \: of \: Triangle \: ( BC ) = 40 \: cm}}$

Not sure about the answer ?

Let's Verify to confirm :

Now, we know

The three sides , so let's plug the values in the formula :-

$:\implies \sf AC^{2} = AB^{2} + BC^{2}$

$:\implies \sf 41^{2} = 9^{2} + 40^{2}$

$:\implies \sf 1681 = 81 + 1600$

$:\implies \sf 1681 = 1681$

${\underline{\sf {L.H.S = R.H.S}}}$

Hence,

Verified !!

Therefore, the third side of the given right angled triangle is 40 cm.