Question

find the perimeter of a right angled triangle whose hypotuse is 41 cm and breath is 40 cm​

Answer 1

Answer:

90cm.

Explanation :

We know that,

Perimeter of a triangle : sum of all sides

We are given with two sides :

• Hypotenuse - 41cm
• Base - 20cm

We require the third side to calculate it's perimeter.

Since, it's a right angled triangle.

Using Pythagoras theorem,

→ 41² = 40² + third side²

• Taking third side as ‘p’

→ 1681 = 1600 + p²

→ 1681 - 1600 = p²

→ 81 = p²

→ √81 = p

→ 9 = p

∴ The third side is 9cm.

So, the perimeter is : 41 + 40 + 9

= 90cm.

Required answer : 90cm.

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: answer:-}}}}}$

★GIVEN:-

• Hypotenuse = 41 cm

• Base = 40 cm

★TO FIND:-

• Perimeter

★FORMULA USED:-

• $\sf{Hypotenuse^2 = Perpendicular^2 + Base^2}$

• $\sf{Perimeter = H + P + B}$

★SOLUTION:-

$\sf{H^2 = P^2 + B^2}$

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

$: \implies \sf{P^2 = {41}^{2} - {40}^{2} }$

$: \implies \sf{P^2 = 1681 - 1600}$

$: \implies \sf{P^2 = 81}$

$: \implies \sf{P = \sqrt{81} }$

$: \implies \sf{ \boxed{ \underline{ \color{teal}{ \mathsf{ \mathbf{P = 9cm}}}}}}$

Now,

$\sf{Perimeter = H + P + B}$

$\sf{Perimeter = 40 + 41 + 9}$

${ \boxed{ \underline{ \tt{ \huge{ \pink{Perimeter = 90cm}}}}}}$