SOLUTION: The length of a rectangle is 7 cm greater than its width, and a diagonal of the rectangle is 2 cm greater than its length. Find the width of the rectangle

Question 371801: The length of a rectangle is 7 cm greater than its width, and a diagonal of the rectangle is 2 cm greater than its length. Find the width of the rectangle
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
let width be w
..
length = 2w+7
...
diagonal = 2w+7 +2= 2w+9
..
using pythagoras theorem
leg1^2+leg2^2= hypotenuse ^2
w^2+(2w+7)^2=(2w+9)^2
w^2+4w^2+28w+49=4w^2+36w+81
re organize the terms
w^2+28w+49-36w-81+4w^2-4w^2=0
w^2-8w-32=0
solve using quadratic formula
discriminant =192
x1= ((8+sqrt(192))/2
x1= 10.93
x2 is negative
width =10.93 cm
..
m.ananth@hotmail.ca
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