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Answer:
AE = 43.2 units
Perimeter = 229.2 units
Step-by-step explanation:
Let the side AE be 'x'.
Consider triangles AEB and ADC
Statements Reasons
1. ∠ ABE ≅ ∠ ACD Right angles are congruent.
2. ∠A ≅ ∠A Common angle
Therefore, the two triangles are similar by AA postulate.
Now, for similar triangles, the ratio of their corresponding sides are also proportional to each other. Therefore,
Now, plug in the given values and solve for 'x'. This gives,
Therefore, AE = 43.2 units
Now, from right angled triangle ABE,
Similarly from right angled triangle ACD,
Now, perimeter is the sum of all the sides of a figure. Therefore, the perimeter of BCDE is given as:
Perimeter = BE + ED + CD + BC
Perimeter = 27.879 + 72 + 74.344 + 55 = 229.223 ≈ 229.2 (Nearest tenth)
Therefore, the perimeter = 229.2 units