The length of a rectangle exceeds its width by 7inches and the area is 30 square inches what are the length and width of the rectangle'

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The length of a rectangle exceeds its width by 7inches

so

let length = x

and width =y

then , x= y+7....................eq 1

area is 30 square inches

area= length*breadth

=x*y

x*y = 30.................eq 2

now from x= y+7

substitute this value of x in the area equation

so,x*y = 30

(y+7)y=30

y^2+7y -30 =0

y^2+10y-3y -30=0

y(y+10)-3)(y+10)=0

(y+10)(y-3)=0

y= -10 or y=3

since y cannot be negative as it is width

y=3

that is width =3.........................answer

x= y+7

so,x = 3+7

x=10

that is length =10...........................................answer

length = 10 inches

width = 3 inches

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