The length of a rectangle is 5 more than 3 times its width. Find the length and width of the rectangle with an area of 182 square units.
PLEASE EXPLAIN.
Answers
x------------> the length of rectangle
y-----------> the width of rectangle
A----------> area of rectangle
we know that
A= 182 units²
A=x*y ------------> x*y=182 --------> equation 1
and
the length of a rectangle is 5 more than 3 times its width
then
x=5+3*y-------------> equation 2
substitute 2 in 1
(5+3y)*y=182--------> 5y+3y²=182------------> 3y²+5y-182=0
using a graph tool------------> I solve the quadratic equation
see the attached figure
the solution is
y=7
x*y=182-----------> x=182/7----------> x=26
the answer is
the length of rectangle is 26 units
the width of rectangle is 7 units
The length and width of the given rectangle with area of 182 square units is; Length = 26 units and width = 7 units
Area of a Rectangle
Let the length of the rectangle be x
Let the width of rectangle be y
Let the area of rectangle be A
Formula for area of rectangle is;
A = length * width
Thus;
A = xy
We are told that area is 182 square units. Thus;
xy = 182 sq.units -----(eq 1)
Also the length of the rectangle is 5 more than 3 times its width. Thus;
x = 3y + 5 ------(eq 2)
Put 3y + 5 for x in eq 1 to get;
y(5 + 3y) = 182
3y² + 5y = 182
3y² + 5y - 182 = 0
Using online quadratic equation calculator gives; y = 7
Thus; x = 182/7
x = 26
Read more about area of a rectangle at; https://brainly.com/question/13048427
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