Question

Given that the perimeter of the figure ABCD is 149 units, find the value of x. Is triangle ABC~ triangle ADC? Explain.

Answer 1

this is correct answer

Answer 2

The value of x is 11/2 and the quadrilateral ABCD is a kite.

• The perimeter of the given quadrilateral ABCD is given as 149 units.

• Now,

6x + 7x+3 + 9x-8 + 8x-11 = 149

30x = 149 + 16

x = 11/2

• Now,

Length AB = 6x = 33 units

Length BC = 7x + 3 = 83/2 units

Length CD = 9x - 8 = 83/2 units

Length AD = 8x - 11 = 33 units

• Therefore,

length AB = length AD  and length BC = length CD      (Equation 1)

• Now, In ΔABC and ΔADC

length AB = length AD   (From equation 1)

length BC = length CD       (From equation 1)

length AC = length AC   (Common sides)

∴ ΔABC ~ ΔADC   (By SSS test of similarity)

• The given quadrilateral ABCD is a kite as a pair of adjacent sides are congruent.

∴ Quadrilateral ABCD is a kite.