let

x = the original width of the rectangle

3x = the original length of the rectangle (a rectangle is three times as long as it is wide)

the area of the original rectangle is:

A1 = x*3x

the length and the width are each increased by four

x + 4 = the new width

3x + 4 = the new length

the area of the new rectangle is:

A2 = (x + 4)(3x + 4)

since the new area is equal to the old area increased by 176 we hvae

A2 = A1 + 176

(x + 4)(3x + 4) = 3x^2 + 176

by solving we find

x = 10

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3x = 3*10 = 30

the dimensions of the original rectangle are: the length is 30 and the width is 10.