SOLUTION: the perimeter of a rectangle and square are 160 metre each. the area of rectangle is less than that of square by 100 square metre. find the length of rectangle?

Question 869356: the perimeter of a rectangle and square are 160 metre each. the area of rectangle is less than that of square by 100 square metre. find the length of rectangle?

Found 2 solutions by lwsshak3, josgarithmetic:
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
the perimeter of a rectangle and square are 160 metre each. the area of rectangle is less than that of square by 100 square metre. find the length of rectangle?
***
side of square=160/4=40
area of square=40*40=1600
..
let x=length of rectangle
let y=width of rectangle
2x+2y=160
x+y=80
y=80-x
Area of rectangle=x*y=x(80-x)=80x-x^2
Area of square-area of rectangle=100
1600-(80x-x^2)=100
1600-80x+x^2=100
x^2-80x+1500=0
(x-30)(x-50)=0
x=50
or
x=30
length of rectangle=50 m

Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
Assign variables.
s = length of square
x = rectangle length
y = rectangle width
-
Find equations and expressions.
.
.
Area of square, .
Area of rectangle, .
.

SYSTEM OF EQUATIONS:
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4s=160
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2x+2y=160
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s^2-xy=100
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The question is to find length of the rectangle. No distinction is necessary about x or y for length; either one is length or width. First, solve for s and obtain two equations in two unknowns.

, .
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simplified perimeter equation for rectangle.
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eliminated variable s and simplified area equation.

SIMPLIFIED SYSTEM:
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and .

Solve the simplified system.
.

discriminant, .
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General solution for a quadratic equation:

OR

Length of the rectangle can be either 30 OR 50.
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