Question

Find the perimeter of the rectangle whose length is 40 cm and a diagonal is 41 cm.​

Answer 1

Answer:

98cm

Step-by-step explanation:

Using the formulas

P

=

2

(

l

+

w

)

d

=

w

2

+

l

2

Solving for

P

P

=

2

l

+

2

d

2

﹣

l

2

=

2

·

40

+

2

·

41

2

﹣

40

2

=

98

cm

Mark ne as braunliest

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,

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

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

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