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Answer:
Length of the fence required = 135 m
Step-by-step explanation:
Total length of the fence required to cover the vacant lot = Perimeter of the isosceles trapezoid
Perimeter of ABCD = AB + BC + CD + AD
Since, AB = BC = EF = ED = 25 m
From the given right triangle BEC,
m∠EBC = m∠ECB = 45°
ΔBEC will be an isosceles triangle.
So, BE = EC
By Pythagoras theorem,
BC² = BE² + EC²
25² = 2(EC)²
EC = m
And DC = (DF + EF + EC)
= EC + EF + EC [Since, DF = EC]
= 2EC + EF
= 35.4 + 25
= 60.4 m
Hence. perimeter of ABCD = 25 + 25 + 60.4 + 25
= 135.4 m
≈ 135 m
Therefore, length of the fence required = 132 m
