Question

the perimeter P. of any rectangle is given by the formula P = 21 + 2w, where I represents the length if the rectangle and w represents the width. let the length of a rectangle equal 3 ft more than 3 times its width and the perimeter equal 54 ft

Answer 1

width = 6 ft

length = 21 ft

Explanation:

Forming algebraic expressions and finding the dimensions of a rectangle:

Width = w ft

length = 3*w + 3 = (3w + 3) ft

2l +2w = P

2(3w + 3) + 2w = 54

Use distributive property to open the brackets,

2*3w + 2*3 + 2w = 54

6w + 6 + 2w = 54

Combine like terms,

6w + 2w + 6 = 54

8w + 6 = 54

Subtract 6 from both sides,

8w = 54 - 6

8w = 48

Divide both sides by 8

w = 48 ÷ 8

`\sf \boxed{\bf w = 6 \ ft}`

l = 3w + 3

= 3*6 + 3

= 18 + 3

l = 21 ft