Question 165935: The length of a certain rectangle is 4 centimeters longer than its width. And the number of square in its area exceeds 7 times the number of centimeters in its width by 18. Find its dimensions.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The length of a certain rectangle is 4 centimeters longer than its width. And the number of square in its area exceeds 7 times the number of centimeters in its width by 18. Find its dimensions
:
Let x = the width
:
It says,"The length of a certain rectangle is 4 centimeters longer than its width"
Therefore:
(x+4) = the length
then
x(x+4) = the area
:
"And the number of square cm, in its area, exceeds 7 times the number of centimeters in its width by 18."
x(x+4) = 7x + 18
:
x^2 + 4x - 7x - 18 = 0; arrange as a quadratic equation;
:
x^2 - 3x - 18 = 0
Easily factors to:
(x - 6)(x + 3) = 0
Positive solution is what we want here.
x = 6 cm is the width
and
6 + 4 = 10 cm is the length
:
:
Check the solutions, in the statement:
"the number of square cm in it's area exceeds 7 times the number of centimeters in its width by 18."
10 * 6 = 7(6) + 18
60 = 42 + 18; confirms out answer
|
|
|
