Look at the following rectangle:
ΔEDC is equilateral.
Calculate the perimeter of the rectangle.
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Look at the following rectangle:
ΔEDC is equilateral.
Calculate the perimeter of the rectangle.
A rectangle has two pairs of equal opposite sides.
That is:
BC=AD=4
AB=DC
In an equilateral triangle, all sides are equal, therefore:
EC=CD=DE
We know that EC=8, so:
EC=CD=DE=8
We know that:
AB=DC
Therefore:
AB=DC=8
Remember that the perimeter of a rectangle is equal to the sum of all its sides, therefore:
AB+BC+DC+AD
We substitute in all its known sides:
8+4+8+4=
24
24
Calculate the perimeter of the rectangle below.
In any rectangle, opposite sides are equal. So AB = DC and BC = AD. Look at the diagram carefully to identify which sides are opposite to each other.
The equilateral triangle EDC tells us that all its sides are equal. Since EC = 8, then CD = 8 too. This gives us the length of one side of the rectangle!
Use the given information strategically! You know BC = 4 from the diagram, and EC = 8. Since triangle EDC is equilateral, CD must also equal 8.
Add up all four sides of the rectangle: Perimeter = AB + BC + CD + AD. Since AB = CD = 8 and BC = AD = 4, you get: 8 + 4 + 8 + 4 = 24.
Yes! If triangle EDC wasn't equilateral, CD might not equal 8. The equilateral property is crucial for determining that CD = EC = 8.
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