Question

ABCD is parallelogram.
The diagonals AC and BD intersect
at point M. The length of
seg AC, AB and AD is 24, 22 and 34
respectively. Find the length of
seg BD.​

Answer 1

Answer:

length of diagonals of parallelohram is same

so, AC =2 X AM

= 2 X 12

= 24

AC = 24

So, AC similar to BD.

I Think This Answer Help You

Answer 2

Answer:

BD = 52

Step-by-step explanation:

Looking at △ACD

⇒ Sides of triangle are 22, 24 and 34

Find ∠CAD using the cosine rule:

Cosine rule says c² = a² + b² - 2abCosC

22² = 34² + 24² - 2(34)(24)CosC

1632CosC = 34² + 24² - 22²

1632CosC = 1248

CosC = 13/17

C = Cos⁻¹(13/17)

C = 40.12°

⇒∠CAD = 40.12°

Find ∠ACD using the cosine rule:

34² = 22² + 24² - 2(22)(24)CosC

1056CosC = 22² + 24² - 34²

1056CosC = -96

CosC = -1/11

C = Cos⁻¹(-1/11)

C = 95.22°

⇒∠ACD = 95.22°

Find ∠BAD:

∠CAB = ∠ACD = 95.22° (Alternate Angles)

∠BAD =∠CAB  + ∠ADC

∠BAD =40.12 + 95.22 = 135.34°

⇒∠BAD = 135.34°

Find Length BD using cosine rule:

BD² = 34² + 22² - 2(34)(22)Cos(135.34)

BD² = 2704.1

BD = 52

Answer: BD = 52