SOLUTION: Hello and thanks for helping in advance! I appreciate for all your help in your website although I haven't experienced it myself, I have heard a lot of compliments from my friends

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hello and thanks for helping in advance! I appreciate for all your help in your website although I haven't experienced it myself, I have heard a lot of compliments from my friends       Log On


   



Question 686852: Hello and thanks for helping in advance! I appreciate for all your help in your website although I haven't experienced it myself, I have heard a lot of compliments from my friends and other people.
Anyway, here is my question:
Q1: The length of a rectangle is 5 inches longer than the width. if the area of the rectangle is 84 sq. inches, what are the length and width of the rectangle?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width = +w+
The length is +w+%2B+5+
let +A+ = area
+A+=+w%2A%28+w+%2B+5+%29+
+84+=+w%5E2+%2B+5w+
+w%5E2+%2B+5w+-+84+=+0+
use the quadratic formula
+w+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+5+
+c+=+-84+
+w+=+%28-5+%2B-+sqrt%28+5%5E2+-+4%2A1%2A%28-84%29+%29%29+%2F+%282%2A1%29+
+w+=+%28-5+%2B-+sqrt%28+25+%2B+336+%29%29+%2F+2+
+w+=+%28-5+%2B-+sqrt%28+361+%29%29+%2F+2+
+w+=+%28-5+%2B-+19%29+%2F+2+ ( ignore the negative square root )
+w+=+%28+-5+%2B+19+%29+%2F+2+
+w+=+14%2F2+
+w+=+7+
+w+%2B+5+=+12+
The width is 7 in
The length is 12 in
check:
+A+=+w%2A%28+w%2B5+%29+
+84+=+7%2A%28+7+%2B+5+%29+
+84+=+84+
OK