a rectangular room is 4 meters longer than it is wide, and its perimeter is 20 meters. what is the length and width

Answer 1

The perimeter of a rectangle is expressed as 2l + 2w = P. In this case 2l + 2w = 20.

We know that the length is 4m longer than the width. therefore, l = w+4. If we substitute this in for l we get 2(w+4) + 2w = 20.

We must distribute the 2 to make 2w+8+2w = 20.

Now, combine like terms to get 8+4w = 20.

Add 8 to each side and divide by four to solve for w ==> 4w = 12 ==> w = 3

Now, plug in 3 for w in the original equation and solve for l. 2l + 2(3) = 20 ==> 2l + 6 = 20 ==> 2l = 14 ==> l = 7

Therefore the length is 7 meters and the width is 3 meters