A watercolor painting is 15inches long by 9 inches wide. Ramon makes a border around the watercolor painting by making a mat tha
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Answer:
Length of rectangle = 24 inches
Width of rectangle = 1 inches
Step-by-step explanation:
Area of rectangle = 24 square inches
Perimeter of rectangle = 50 inches
Formulas:
Area of rectangle =
Perimeter of rectangle =
where represents length of rectangle and
represents width of rectangle.
So, we can get two equations for and
A) [Area]
B) [ Perimeter ]
Simplifying equation B.
Dividing both sides by 2.
Solving for in terms of width.
Subtracting both sides.
∴
Substituting value of in terms of
in equation A.
Using distribution.
Adding both sides.
subtracting both sides
We have a quadratic equation.
We solve for by factor method.
Splitting middle term into two terms such that the sum of the two = and product of two =
Factoring in pairs.
Factoring as a whole
So, we have
and
By adding 24 to one equation and adding 1 to other we get
and
and
So length can be found out by plugging value of in the length equation.
and
Since length is always the longer side of rectangle so, the dimensions of rectangle can be given by.
length = 24 inches (answer)
width = 1 inches (answer)