The length of a rectangular backyard is eight less than four times the width. The backyard has a perimeter of. 284 feet. Determine the length and width.

Answer 1

Since you are calculating for length and the problem express the Length as 4 times the width less 8, that portion of the equation would be represented by 4w-8 where w represents the width. To calculate perimeter, simply add all the sides. If the width is represented by the variable w and the length is represented by 4w-8, and there are two opposite sides which are congruent, we can set this equation as 2w + 2(4w-8) = 284. Distribute what is in the parentheses first which equals 8w-16 + 2w= 284. Simplified = 10w-16=284. Add 16 to both sides of the equation 10w=300 then divide each side by 10 and w=30. Plug 30 in for w in the above equation to check. 60+ 2(4(30)-8)=284. Simplified that equals 60+2(112)=284, 60+224=284, 284=284 Don’t forget your label! P=284ft

Answer 2

So Amy C.,

Put a variable in tr represent width, and translate all your info to equations -- this is what you do to solve ANY word problem. You can express length in terms of the width -- that's one equation. Then, you can express the perimeter in terms of length and width (I really hope you can!). Then you can solve the equation for perimeter = 284 . That's one equation in one variable!

-- Cheers, -- Mr. d.