In a ABC, the bisector of A divides BC into segment BD with a length of 28 units and segment DC with a length of 24 units. If AB = 31.5 units, what could be the length of AC?

A. There is not a enough information to determine the length of AC

B. 21.333 units

C. 27 units

D. 36.75 units

Solved

Show answers

Ответ:

leomessifanboy678

07.12.2022

Mathematics

I'll choose 'x' variable first to eliminate because -

-3 (coefficient of 'x' in Eqn.1) & 3 (coefficient of 'x' in Eqn.2) are additive inverses of each other , so they can be easily eliminated by simply adding those equations. It can be also solved by using elimination method but you'll need to multiply -1 with either Eqn.1 or Eqn.2 because in elimination method , a variable can be eliminated only when their coefficients are numerically equal (along with their sign).

Step-by-step explanation:

Eqn.1 → -3x - 8y = -24

Eqn.2 → 3x - 5y = 45

If we'll add both the equations , then '3x' would be getting cancelled first.

⇒ (-3x - 8y) + (3x - 5y) = (-24) + (45)

⇒ 3x - 3x - 8y - 5y = 45 - 24

⇒ -13y = 21

⇒ $y = \frac{-21}{13}$

Putting the value of y in eqn.2 ,

⇒ $3x - 5(\frac{-21}{13}) = 45$

⇒ $3x + \frac{105}{13} = 45$

⇒ $3x = 45 - \frac{105}{13}$

⇒ $3x = \frac{585 - 105}{13} = \frac{480}{13}$

⇒ $x = \frac{480}{13 \times 3} = \frac{480}{39}$

Reducing the fraction gives ,

⇒ $x = \frac{160}{13}$

0,0(0 оценок)

Ask your question to the AI advisor

Ai-bot is an expert in any field and is the perfect companion for reliable and useful answers and advice on a variety of topics, including science, history, technology, art, sports, health, culture and more.

Ask your question

More tips

Answers on questions: Mathematics

Ask an AI advisor a question

I want advice

In a ABC, the bisector of A divides BC into segment BD with a length of 28 units and segment DC with a length of 24 units. If AB = 31.5 units, what could be the length of AC? A. There is not a enough information to determine the length of AC B. 21.333 units C. 27 units D. 36.75 units