Find the value of DE.
2 answers:
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Answer:
<u>Problem 1:</u>
x = 12 unit ; y = 120 ; z = 60 ; perimeter = 58 unit
<u>Problem 2:</u>
FG = 16 unit ; EG = 2√153 unit ; y = 5 unit
Step-by-step explanation:
<u>Problem 1</u>
Since ABCD is a parallelogram. so,
∠ABC = ∠ADC [Since opposite angles of a parallelogram are equal]
but, ∠ADC = 120° [given]------------(1)
So, ∠ ABC = y° = 120° ----------------(2)
Again, sum of two consecutive angles of a parallelogram is, 180°, so,
∠BCD + ∠ADC = 180°
So, ∠BCD =z° = 180° - 120° = 60° [Putting the value of ∠ADC from (1)]-----(3)
Again, since opposite sides of a parallelogram are equal,
so, BC = AD
⇒ (x + 5) = 17
⇒ x = 12------------------------(4)
So, AB = 12 unit , AD = 17 unit
So, the perimeter of the parallelogram is given by,
2(AB + AD)
= unit
= 58 unit --------------------------------------------------------------(5)
<u>Problem 2</u>
Perimeter of parallelogram EFGH = 52 unit
So, 2(EH + GH) = 52 unit
⇒ 2 ( x + x + 6) = 52
⇒ 4x = 40
⇒ x = 10
Now, FG = EH [since opposite sides of a parallelogram are equal]
= (x + 6) unit
= (10 + 6) unit = 16 unit ------------------------------(1)
Again for a parallelogram, the diagonals bisect each other.
so, EG =
= 2√153 unit -----------------------------------------(2)
and,
3y - 10 = y
⇒ y = 5 -----------------------------------------------(3)