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Answer:
The perimeter and area of the square are 56 units and 196 square units, respectively.
Step-by-step explanation:
The inner right triangle represents a 45-45-90 right triangle, which has the feature of a hypotenuse whose length is time the length of any of its legs. If the hypotenuse has a measure of
, then the legs of the triangle have a measure of
.
Now, we are aware that the side length of the square is twice the length of the leg of the right triangle. Then, side length of the square is 14 units long.
Lastly, we know from Geometry that the perimeter and area of the square are represented by the following expressions:
Perimeter
(1)
Area
(2)
Where is the side length of the square.
If we know that , then the perimeter and area of the square are, respectively:
The perimeter and area of the square are 56 units and 196 square units, respectively.