Question 951943: A rectangle has a perimeter of 86 and an area of 252. Its length is 8 more than 4 times its width. Write and solve a system of equations to find the dimensions of the rectangle.
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let's call the width w and the length l.
The perimeter is 86 and the area 252.
And the problem states that the length is 4w+8.
Perimeter: 2w + 2l = 86
Area : w x l = 252
Now let's solve one at the time. Since we know that l = 4w+8, let's substitute:
2w + 2(4w+8) = 86 Multiply on left:
2w + 8w + 16 = 86 Add on left and subtract 16, both sides:
10w = 70 Divide by 10, both sides:
w = 7
The width is: 7 and the length 4(7) + 8 = 36
Let’s see:
2w + 2l = 86
2(7) + 2(4(7)+8) = 86 (remember the order of operations 1)multiply inside, 2) clear parentheses, etc.)
14 + 72 = 86
86 = 86 We’ve got the correct answer.
Now the area:
w x l = 252
7 x 36 = 252
252 = 252 Again, we’ve got the right answer.
|
|
|
