Question

find the length and breadth of the rectangular plate whose area is 60 m square and its perimeter is 32 metre​

Answer 1

AnswEr:

• When Breadth is 6 m, Length be 10 m
• When Breadth is 10 m, length be 6 m.

ExplanaTion:

Given:

• Area of rectangular plot = 60 m²
• Perimeter of rectangular plot = 32 m

To find:

• Length and breadth of rectangular plot

Solution:

Let length be L and breadth of B of rectangular plot.

We know that,

$\large{\boxed{\rm{\red{Perimeter\:of\:rectangle\:=\:2(L+B)}}}}$

: $\implies$ 2( L + B ) = 32

: $\implies$ L + B = $\sf{\cancel{\dfrac{32}{2}}}$ $\small{\sf{16}}$

: $\implies$ L + B = 16

: $\implies$ L = 16 - B...........(1)

We also know that,

$\large{\boxed{\rm{\green{Area\:of\:rectangle\:=\:L\:\times\:B}}}}$

: $\implies$ 60 = L × B.............(2)

$\small{\sf{\: \: \: \:Substitute\:the\:value\:of\:(1)\:in\:(2)}}$

: $\implies$ 60 = ( 16 - B ) B

: $\implies$ 16B - B² = 60

: $\implies$ - B² + 16B - 60 = 0

: $\implies$ B² - 16B + 60 = 0

$\small{\sf{\: \: \: \:Splitting\:middle\:term,\:we\:get,}}$

: $\implies$ B = 10 and 6.

$\rule{200}2$

Put the value of B in (1).

• When B = 6 m

: $\implies$ Length = 16 - 6

: $\implies$ Length = 10 m

• When B = 10 m

: $\implies$ Length = 16 - 10

: $\implies$ Length = 6 m

Answer 2

$\huge \red { \bigstar{ \underline{ÀNSWER♡}}}$

$\huge{ \blue {\ddot { \blue{ \smile}}}}$

When Breadth is 6 m, Length be 10 m

When Breadth is 10 m, length be 6 m.

$\large{ \boxed{ \fbox{given}}}$

Area of rectangular plot = 60 m²

Perimeter of rectangular plot = 32 m

$= >$

Let length be L and breadth of B of rectangular plot.

We know that,

$\large { \boxed{ \green{perimiter \: of \: rectangle = 2(l + b)}}}$

$2( L + B ) = 32$

$l + b = \sf{ \cancel{ \dfrac{32}{2}}}$

$= \small{\sf{16}}$

$\implies \: L + B = 16$

$= > L = 16 - B...........(1)$

As We also know that,

$\large{\boxed{\rm{\green{Area\:of\:rectangle\:=\:L\:\times\:B}}}} </p><p>$

=> 60 = L × B.............(2)

substituting 1 in equation 2,

=> 60 = ( 16 - B ) B

=>16B - B² = 60

=> - B² + 16B - 60 = 0

=>B² - 16B + 60 = 0

Now,

=> B = 10 and 6.

Putting value of B in (1)

when, B = 6 m

=>Length = 16 - 6

=> Length = 10

=> when B = 10 m

=>Length = 16 - 10

=>Length = 6 m

_______________________________________

hops this may help you

$\huge{ \red{ \ddot{ \smile}}}$

$\huge \blue{ \mathfrak{thanks♡</p><p>}}$