The length of a rectangle is 8cm more than 3 times its width. The perimeter of the rectangle is 64cm.

Question

I need to figure out the length, width, and height.

Answer 1

Find what you know.

Perimeter = 64cm

Length = width*3 + 8cm

Width = unknown (use w)

Perimeter of a rectangle formula is:

P = 2*L + 2*W or P = 2(L + W)

We know P and we have a formula for L

64cm = 2[(w*3 + 8cm) + w]

64cm = 2(3w + 8cm) + 2w

64cm = 6w + 16cm + 2w

 

Combine like terms:

64cm = 8w + 16cm

 

Subtract 16cm from both sides:

64cm - 16cm = 8w

48cm = 8w

 

Divide both sides by 8 to isolate the variable.

48cm/8 = w

6cm = w or swap them and w = 6cm

 

Now take the formula for perimeter again and plug in the value for width

 

64cm(P) = 2(L + 6cm(W))

64cm = 2L + 12cm

 

Subtract 12cm from both sides:

64cm - 12cm = 2L

52cm = 2L

 

Divide both sides by 2 to isolate the variable:

52cm/2 = L

26cm = L or swap them and L = 26cm

 

Rectangle is 26cm in length and 6cm in width.  There is no height variable in a 2D rectangle, but sometimes (rarely) width is referred to as height. If this is a 3D box, than the height is equal to the width, in which case the information given might be slightly misleading.

Answer 2

The perimeter = 2l + 2w

l = 3w+8

2l+2w = 64

2(3w+8)+2w = 64

6w+2w+16 = 64

8w + 16 = 64

8w = 48

w = 6 so l = 3(6)+8 = 26