A square has its length increased by 5 meters and its width decreased by 3 meters. The resulting rectangle has an area of 180 meters. a. What was the perimeter of the original square? b. What was the are of the original square?

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c. what is the perimeter of the rectangle?

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Answer 1 · 2018-03-17T09:16:48

a. The Perimeter of the Square #4xx13=52# mtr.

b. The Area of the Square #13^2=169# sq. mtr.

c. The Perimeter of the Rectangle #2{(13+5)+(13-3)}=56# mtr.

Suppose that, the length of each side of the square is #x#

meters.

Now, after the changes, the length and the width become #(x+5)#

and #(x-3)# meters resp.

Hence, the area of the rectangle is #(x+5)(x-3)# sq. mtr.,

which is given to be #180# sq. mtr.

#:. (x+5)(x-3)=180#.

#:. x^2+2x-15=180, or, x^2+2x=195#.

#:. x^2+2x+1=195+1=196#.

#:. (x+1)^2=14^2#.

#:. x+1=+-14#.

#:. x=+-14-1, i.e., #

# x=13, or, x=-15#, which is not admissible.

#:. x=13#.

Hence, a. The Perimeter of the Square #4xx13=52# mtr.

b. The Area of the Square #13^2=169# sq. mtr.

c. The Perimeter of the Rectangle #2{(13+5)+(13-3)}=56# mtr.

Enjoy Maths.!