SOLUTION: A small painting has an area of 400 cm 2 . The length is 4 more than 2 times the width. Find the dimensions of the painting. Solve by completing the square. Round answers to

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: A small painting has an area of 400 cm 2 . The length is 4 more than 2 times the width. Find the dimensions of the painting. Solve by completing the square. Round answers to       Log On


   

Question 585163: A small painting has an area of 400 cm 2 . The length is 4 more than 2 times the width. Find the dimensions of the painting. Solve by completing the square. Round answers to the nearest tenth of a centimeter.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +w+ = the width
+w+%2B+4+ = the length
given:
+w%2A%28+2w+%2B+4+%29+=+400+ cm2
+2w%5E2+%2B+4w+=+400+
+w%5E2+%2B+2w+=+200+
Complete the square:
+w%5E2+%2B+2w+%2B+%282%2F2%29%5E2+=+200+%2B+%282%2F2%29%5E2+
+w%5E2+%2B+2w+%2B+1+=+200+%2B+1+
+%28+w+%2B+1+%29%5E2+=+201+
+w+%2B+1+=+sqrt%28+201+%29+
+w+%2B+1+=+14.177+
+w+=+13.177+
+2w+%2B+4+=+26.354+%2B+4+
+2w+%2B+4+=+30.354+
The width is 14.2 cm
The length is 30.3 cm
check answer:
+w%2A%28+2w+%2B+4+%29+=+400+
+13.177%2A30.354+=+400+
+399.975+=+400+
close enough