The length of a rectangle is three times as long as its width. The width of this rectangle is 6 inches smaller than its length. Find the length and the width. (It would also be interesting to know its area and perimeter!)

The length is 9in and the width is 3in

The perimeter is 24in and the area is 27in²

Step-by-step explanation:

To start we have to make 2 equations with the information that gave us the problem

l = length

w = width

w = l - 6in

l = 3w

we replace l in the first equation with (3w)

w = (3w) - 6in

w - 3w = -6in

-2w = -6in

w = -6in / (-2)

w = 3in

now we replace the value of w in the second equation

l = 3w

l = 3 (3in)

l = 9in

Now that we have the length and width we can calculate the perimeter and the area with the following formulas

p = perimeter

a = area

p = 2w + 2h

p = 2(3in) + 2(9in)

p = 6in + 18in

p = 24in

a = w * l

a = 3in * 9in

a = 27in²

i believe the correct answer is b.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)