Question

I am rectangle.my length is x unit and breadth is y unit . Sum of my length and breadth =36.My breadth is 5/7 times of the length. The difference between my length and breadth is 6 unit. If the breadth is subtracted twice the length, the answer is 27. ​

Answer 1

Solution :-

given that,

→ x + y = 36 -------- Eqn.(1)

→ y = (5/7)x ------- Eqn.(2)

→ x - y = 6 -------- Eqn.(3)

Adding Eqn.(1) and Eqn.(3)

→ x + y + x - y = 36 + 6

→ 2x = 42

→ x = 21 .

putting value of x in Eqn.(1)

→ 21 + y = 36

→ y = 36 - 21

→ y = 15 .

checking now,

→ 2 * length - breadth = 27

→ 2 * 21 - 15 = 27

→ 42 - 15 = 27

→ 27 = 27 .

Answer 2

Given: The length and breadth of a rectangle are x and y units respectively Sum of my length and breadth = 36 and My breadth is 5/7 times of the length.

⠀⠀⠀⠀•The difference between my length and breadth is 6

⠀⠀⠀⠀• If the breadth is subtracted twice the length is 27

To be Found : The length and breadth of the rectangle

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀

❒ Let the length of the rectangle be x and the breadth be y respectively.

${ \underline{ \bf{ \bigstar \:According \: to \: the \: question : }}}$

$\longrightarrow \tt \: x + y = 36 - - - - (1) \\ \\ \\ \longrightarrow \tt \: y = \frac{5}{7} x - - - - (2) \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: x - y = 6 - - - - (3) \:$

★ Now,

• Let's add up equation 1 and equation 3 to find the value of x

$\longrightarrow \tt \: x \:\cancel{ + y} + x \: \cancel{- y} = 36 + 6 \\ \\ \\ \longrightarrow \tt2x = 42 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: x = \frac{42}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \longrightarrow \tt \: { \purple{ \underline{ \boxed{ \frak{x = 21}}} \star}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• Now, let's substitute the value of x in any of the equation to find the value of y

★ Putting it in equation 3 we get,

$\longrightarrow \tt \: x - y = 6 \\ \\ \\ \longrightarrow \tt \: 21 - y = 6 \\ \\ \\ \longrightarrow \tt - y = 6 - 21 \\ \\ \\ \longrightarrow \tt - y = - 15 \: \: \\ \\ \\ \longrightarrow \tt \: { \purple{ \underline{ \boxed{ \frak{y = 15}}} \star}} \: \: \: \:$

${ \large{ \underline{ \pmb{ \rm{Verification... }}}}}$

${ : \implies} \sf \: y = ( \frac{5}{7} )x \: \: \: \: \: \: \: \\ \\ \\ { : \implies} \sf \: 15 = \frac{5}{7} \times 21 \\ \\ \\ { : \implies} \sf15 = 5 \times 3 \: \: \: \\ \\ \\ { : \implies}{ \boxed{ \frak{15 = 15}} \star} \: \:$

• L.H.S = R.H.S Hence Verified.!!

Henceforth,

${ \underline{ \frak{The \: lenght \: and \: breadth \: are \: 21 \: and \: 15 \: respectivly}}}$

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