Question

The length of a rectangle is 2 inches more than 4 times the width. The perimeter is 64 inches. Find the length and the width.

Answer 1

Length of the rectangle = 26 inch

Width of the rectangle = 6 inch

Step-by-step explanation:

Let the width of the rectangle be ‘ w ‘

Length of the rectangle

l = 4 w + 2 inches

Perimeter of a rectangle = 2 time of sum of its length and width

= 2 ( w + l) ------------------------equation (1)

Substituting the value of l in equation 1, we get –

2 (w + (4 w + 2)) = 64 inches

2w + 8w + 4inches = 64 inches

10w = 64 inches - 4inches

10 w = 60 inches

w = 6 inches

Length of the rectangle = 4w + 2inch

= 4 x 6 inches + 2 inch

= 24 inch + 2 inch

= 26 inch

Thus,

Length of the rectangle = 26 inch

Width of the rectangle = 6 inch

Answer 2

The width is 6 inches and the length is 26 inches.

Step-by-step explanation:
L=4w+2, since the length is 2 more than 4 times the width.

The perimeter is given by P=2L+2w; using our equation for L, we have
P=2(4w+2)+2w.

Using the distributive property, we have
P=2*4w+2*2+2w
P=8w+4+2w.

Combining like terms, we have P=10w+4.

We know the perimeter is 64, so we have
64=10w+4.

Subtract 4 from both sides:
64-4=10w+4-4
60=10w.

Divide both sides by 10:
60/10 = 10w/10
6=w.

Substitute this into the equation for length: L=4*6+2=24+2=26