Question

Q.A rectangular park is to be designed whose breadth is 3m less than its length.
Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude (see figure in the above attachment).Find its length and breadth.

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Answer 1

Answer:

Therefore, its area =1/2× x × 12 = 6 x m2. So, the breadth of the park = 4m and its length will be 7m.

Step-by-step explanation:

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Answer 2

Given :-

A rectangular park is to be designed whose breadth is 3m less than its length. Its area is to be 4 square metres more than the area of a park that has already been made in the shape of an isosceles triangle with its base as the breadth of the rectangular park and of altitude .

To Find :-

Length and Breadth of the Rectangular park .

Solution :-

Let's say the length of the rectangular park be "x metre" .Now According To Question ;

=> Breadth of the Rectangular Park = ( x - 3 ) m = ( b )

=> Length of the Rectangular Park = ( x ) m = ( l )

=> Base of isosceles triangular Park = ( x - 3 ) m = ( b )

=> Altitude of triangular Park = 12 m = ( a )

Again , According To Question ;

=> ( l × b ) = [ 1/2 × a × b ] + 4

=> { x ( x - 3 ) } = [ 1/2 × 12 × ( x - 3 ) ] + 4

=> x² - 3x = [ 6 ( x - 3 ) ] + 4

=> x² - 3x = 6x - 18 + 4

=> x² - 3x - 6x = - 14

=> x² - 9x + 14 = 0

=> x² - 7x - 2x + 14 = 0

=> x ( x - 7 ) - 2 ( x - 7 ) = 0

=> ( x - 7 ) ( x - 2 ) = 0

=> Either , x - 7 = 0 or x - 2 = 0

=> x = 7 or x = 2

But x can't be 2 . Because if x = 2 . Then , Base of the park becomes ( x - 3 ) = ( 2 - 3 ) = ( -1 ) .

Hence. ,x = 2 ( rejected )

Now , x = 7

So , Length of rectangular park = x = 7 m

Breadth of Rectangular Park = x - 3 = 7 - 3 = 4m

Henceforth , The Length and breadth of the rectangular park are 7m and 4m respectively .