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meriva
2 years ago
9

Kindly solve this please!Diagram for both the questions are given.​

Mathematics
2 answers:
klio [65]2 years ago
5 0

Answer:

9)  B. 8

10)   D. 4.5

Step-by-step explanation:

<u>Question 9</u>

For ease of visualization, label the <u>different legs</u> of the journey on the diagram (see attachment).

The journey needs to <u>start and end at point A</u>, go through <u>points B and C</u> (in any order), and <u>not travel any road twice</u>.

The <u>different routes </u>are:

  • AB (u), BC (x), CA (w)
  • AB (u), BC (y), CA (w)
  • AB (u), BC (x), CA (z)
  • AB (u), BC (y), CA (z)
  • AC (w), CB (x), BA (u)
  • AC (z), CB (x), BA (u)
  • AC (w), CB (y), BA (u)
  • AC (z), CB (y), BA (u)

Therefore, there are 8 different routes.

<u>Question 10</u>

Triangles EDC and EAB are similar since they have congruent angles:

  • ∠EDC ≅ ∠EAB  (both right angles)
  • ∠DEC ≅ ∠AEB  (vertical angle theorem)

Therefore, their <u>corresponding sides</u> are in proportion.

⇒ CD : BA = ED : EA

⇒ 9 : 3 = ED : EA

⇒ 3 : 1 = ED : EA

Since we know that AD = 4:

⇒ ED = 3

⇒ EA = 1

<u>Area of a triangle</u>

\sf Area = \dfrac{1}{2} \times base \times height

To find the area of triangle AEC, <u>subtract</u> the area of triangle EDC from the area of triangle ADC.

\begin{aligned}\textsf{Area of triangle AEC} & = \sf Area\:of\:\triangle ADC - Area\:of\:\triangle EDC\\& = \sf \dfrac{1}{2} \cdot CD \cdot AD-\dfrac{1}{2} \cdot CD \cdot ED\\& = \sf \dfrac{1}{2}(9)(4)-\dfrac{1}{2}(9)(3)\\& = \sf 18-13.4\\& = \sf 4.5\:\:units\:squared\end{aligned}

Learn more about similar triangles here:

brainly.com/question/21427237

Bogdan [553]2 years ago
3 0

Answer:

  • Q9 - B) 8
  • Q10 - D) 4.5

========================

<h2>Question 9</h2>

We have a diagram and need to find the number of routes without repeat paths:

  • ABCA or ACBA

We can see that there is one route from A to B, two routes from B to C and two routes from C to A. This is same on reverse order.

This gives us the number of routes:

  • ABCA = 1*2*2 = 4
  • ACBA = 2*2*1 = 4

Total number is:

  • 4 + 4 = 8

The matching answer choice is B

---------------------------------------------------------------------------

<h2>Question 10</h2>

From the given we can observe that:

ABC and DCE are similar triangles, since they have same angle at vertex E (vertical angles are equal) and both are right triangles.

From similarity we get same ratio of corresponding sides:

  • AE/DE = AB/CD = 3/9 = 1/3

We can find areas of triangles ACD and ECD and subtract to get the area of triangle AEC:

  • S_{ACD} - S_{ECD} = S_{AEC}

As per ratio of corresponding sides:

  • AE/DE = 1/3

As per segment addition:

  • AE + DE = AD = 4

From the two equations above we get:

  • DE = 3/4*AD = 3/4*4 = 3

Now, the required area is:

  • S_{ACD} - S_{ECD} = 1/2(4*9) - 1/2(3*9) = 4.5

This is matching the answer choice D

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