Question

Find the length and width of a rectangle of area A= 198 in^2 if its width= x and its length= x + 7.

Answer 1

Answer:

Length: 18

Width: 11

Step-by-step explanation:

Step 1: Write out equation

x(x + 7) = 198

Step 2: Distribute

x² + 7x = 198

Step 3: Complete the square

x² + 7x + 49/4 198 + 49/4

(x + 7/2)² = 841/4

Step 3: Solve for x

√(x + 7/2)² = √(841/4)

x + 7/2 = ±29/2

x = -7/2 ± 29/2

x = 11, -18

Since you can't have negative length, your x will be 11. Now simply plug them in as width and length:

Width = x

x = 11 in

Length = 11 + 7

x = 18 in

And we have our final answers!