Math, asked by Tarzan6300, 10 months ago

Sum of length and breadth e is 14 Area is 48 find diagonal

Answers

Answered by Anonymous
28

let x and y be the sides of the rectangle.

Then the area is xy = 48

By Pythagoras’s theorem, x^2 + y^2 = 10^2 = 100

Then (x + y)^2 = x^2 + y^2 + 2xy = 100 + 2*48 = 196

So the perimeter is 2(x + y) = 2 sqrt(196) = 28

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Answered by Anonymous
16

\huge\mathfrak\blue{Answer:}

Given:

  • We have been given rectangle whose area is 48cm²
  • Sum of length and breadth of rectangle is 48cm²

To Find:

  • We have to find the measure of diagonal of the given rectangle

Solution:

Let the length of rectangle = x

Breadth of rectangle = y

According to the Question

\implies x + y = 14

\implies y = ( 14 - x ) _______( 1 )

_________________________________

Also we have

\implies Area = 48 cm²

\implies (Length) x (Breadth) = 48 cm²

\implies xy = 48 cm²

Putting value of y from equation ( 1 )

\implies x ( 14 - x ) = 48

\implies 14x - x² = 48

\implies x² - 14x + 48 = 0

Solving the Equation using Middle Term Splitting Method

\implies x² - 8x - 6x + 48 = 0

\implies x ( x - 8 ) - 6 ( x - 8 ) = 0

\implies ( x - 8 ) ( x - 6 ) = 0

Hence Either x = 8 or x = 6

_______________________________

\huge\mathfrak\red{Case1:}

\fbox{When x = 8}

\implies y = 14 - x

\implies y = 14 - 8

\implies \fbox{y = 6}

\huge\mathfrak\red{Case2:}

\fbox{When x = 6}

\implies y = 14 - 6

\implies \fbox{ y = 8}

_______________________________

Either x = 8 and y = 6 or Vice Versa

Let the Diagonal of rectangle = D cm

Using Pythagoras Theorm

\implies ( D )² = ( x )² + ( y )²

\implies D² = ( 8 )² + ( 6 )²

\implies D² = 64 + 36

\implies D² = 100

Taking square root on both sides

\implies D = \sqrt{100}

\implies \fbox{D = 10 cm}

Diagonal of Rectangle is 10 cm

________________________________

\huge\mathfrak\red{Verification:}

\fbox{Sum = 8 + 6 = 14 cm}

\fbox{Area = 8 \times 6 = 48 }

Hence Verified !!

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