Question

Help.. or die.. you decide.

Answer 1

Answer:

Problem 1:

x = 12 unit ; y = 120 ; z = 60 ; perimeter = 58 unit

Problem 2:

FG = 16 unit ; EG = 2√153 unit ; y = 5 unit

Step-by-step explanation:

Problem 1

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)

= $2 \times (12 + 17)$  unit

= 58 unit --------------------------------------------------------------(5)

Problem 2

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 = $2 \times \sqrt{153}$

           = 2√153 unit -----------------------------------------(2)

and,

3y - 10 = y

⇒ y = 5 -----------------------------------------------(3)