Question

If the length of a rectangle is decreased by 2 metres and the breadth increased by 2 metres the area would increase 8 square metres. If the length is decreased by 3 metres and the breadth decreased by 1 metre,the area would decrease by 27 square metres.what are the length and breadth?
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Answer 1

Answer:

Your answer is (Length= 12m)(Breadth=6m)

Explanation:

Let the length be x

& the breadth be y

Area= LxB

=(x)(y)

= xy

Condition when the length decrease and breath increase. Area increase 8 square metres

Length= x-2

Breadth= y+2

Area=(x-2)(y+2)

xy+2x-2y-4 = xy+8

xy-xy+2x-2y-4-8 = 0

2x-2y-12=0 (i) equation

condition when the length and breadth decrease. Area decrease by 27 square metres

Length= x-3

Breadth= y-1

Area= (x-3)(y-1)

xy-x-3y+3 = xy-27

xy-xy-x-3y+3+27=0

-x-3y+30=0 (ii) equation

Using Elimination Method

2x-2y-12=0 (i) equation

-x-3y+30=0 (ii) equation

multiplying first equation with -1 and second equation with 2

2x-2y-12=0}x-1

-x-3y+30=0}x2

-2x+2y+12=0 (iii) equation

-2x-6y+60=0 (iv) equation

for the next step see the picture given above

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Answer 2

Given: If the length of a rectangle is decreased by 2 metres and the breadth increased by 2 metres the area would increase 8 square metres. If the length is decreased by 3 metres and the breadth decreased by 1 metre, the area would decrease by 27 square metres.

To find: The length and breadth.

Solution:

• Let the length and breadth be x metre and y metre, respectively.
• The area of a rectangle is given by the following formula.

        $A = l * b$

            $= xy$

• When the length is decreased by 2 metres and the breadth increases by 2 metres, the area increases by 8 m².

        $A_{1} = (x-2) m * (y+2) m$

        $(A+8) m^{2} = xy +2x-2y-4$

        $(xy+8) m^{2} = xy +2x-2y-4$

• On simplifying the equation formed,

        $x - y = 2$

• When the length is decreased by 3 metres and the breadth decreased by 1 metre, the area decreases by 27 m².

        $A_{1} = (x-3) m * (y-1) m$

        $(A - 27) m^{2} = xy -x-3y+3$

        $(xy- 27) m^{2} = xy -x-3y+3$

• On simplifying the equation formed,

        $x + 3y = 30$

• On solving the two of equations obtained simultaneously, the value of x and y are found to be,

        $x = 6 m$

        $y = 4 m$

Therefore, the length and breadth is 6 m and 4 m, respectively.