Question 1207600: Hello dear tutor, help me solve this problem.
If the area of a rectangle is 42 squared unit and the perimeter is 26.
Find the length and width of the rectangle.
Answer by Timnewman(323)   (Show Source):
You can put this solution on YOUR website! To find the length and width of the rectangle, we can use the formulas:
Area = Length x Width
Perimeter = 2(Length + Width)
Given:
Area = 42 square units
Perimeter = 26 units
Let's start by using the perimeter formula:
26 = 2(Length + Width)
Divide both sides by 2:
13 = Length + Width
Now, let's use the area formula:
42 = Length x Width
Since Length + Width = 13, we can rewrite the area formula as:
42 = (13 - Width) x Width
Expand and simplify:
42 = 13W - W^2
W^2 - 13W + 42 = 0
Factor the quadratic equation:
(W - 6)(W - 7) = 0
This gives us two possible values for Width:
W = 6 or W = 7
Now, we can find the corresponding Length values:
If W = 6, then Length = 13 - 6 = 7
If W = 7, then Length = 13 - 7 = 6
So, the length and width of the rectangle are:
Length = 7 units, Width = 6 units
or
Length = 6 units, Width = 7 units
Both solutions are valid, and the rectangle can be oriented either way.
Best of luck.
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