Adithi S.

To divide a line segment of 7.6 cm into two parts in the ratio 5:8, the segment is divided into a total of 5+8=13 parts.

The length of each part is 7.6 cm/13 ≈0.5846cm

• The length of the first part (5 parts) is 5×7.6 cm/13 ≈2.923cm
• The length of the second part (8 parts) is 8×7.6 cm/13 ≈4.677cm

Verifying the Sum:

2.923 cm+4.677 cm≈7.6 cm

I'll provide a step-by-step guide on how you can draw these triangles using basic geometry tools:

• Ruler
• Compass
• Pencil
• Protractor (optional for verifying angles)

First Triangle (sides 5cm, 6cm, 7cm) Construction:

1. Draw the Base (5 cm):

   • Draw a horizontal line segment AB of length 5 cm.

2. Draw an Arc (6 cm):

   • Place the compass at point A.
   • Measure 6 cm on the compass.
   • Draw an arc above the line segment AB.

3. Draw an Arc (7 cm):

   • Place the compass at point BBB.
   • Measure 7 cm on the compass.
   • Draw another arc intersecting the first arc.

4.  Mark the Intersection (Point C):

   • Label the intersection point of the arcs as C.

5. Complete the Triangle:

   • Draw line segments AC and BC to complete the triangle ABC.

Second Triangle (sides 4/5th of Frist Triangle) Construction:

1. Calculate the Scaled Sides: The sides of the scaled triangle are 4/5 of the corresponding sides of the first triangle.

• 4/5×5 cm=4cm
• 4/5×6 cm=4.8cm
• 4/5×7 cm=5.6 cm

2. Measure and Draw the Scaled Sides:

1. Draw the Base (4 cm):
   Draw a horizontal line segment DE of length 4 cm.

2. Draw an Arc (4.8 cm):

   • Place the compass at point D.
   • Measure 4.8 cm on the compass.
   • Draw an arc above the line segment DE.

3. Draw an Arc (5.6 cm):

   • Place the compass at point E.
   • Measure 5.6 cm on the compass.
   • Draw another arc intersecting the first arc.

4. Mark the Intersection (Point F):

   • Label the intersection point of the arcs as F.

5. Complete the Triangle:

   • Draw line segments DF and EF to complete the triangle DEF.

a) Average speed is defined as the total distance traveled divided by the total time taken to travel that distance. Mathematically, it can be expressed as:

Average speed=Total distance/Total time

(b) To calculate the average speed for the entire journey of the bus, we need to determine the total distance traveled and the total time taken for the round trip.

1. Total Distance: The bus travels a distance of 120 km to the destination and then returns the same distance back. Therefore, the total distance, D = 120km + 120km = 240km

2. Total Time: To find the total time, we need to calculate the time taken for each leg of the journey separately and then sum these times. 

   Time to travel to the destination: The bus travels 120 km with a speed of 40 km/h.

   t1=Distance/Speed=120 km/40 km/h=3 hours

   Time to return: The bus returns the same 120 km distance with a speed of 30 km/h.

   t2=DistanceSpeed=120 km30 km/h=4 hours
   
   

   Therefore, the total time,T for the round trip is:

   T=t1+t2=3 hours+4 hours=7 hours

3. Average Speed: Using the formula for average speed: Average speed=Total distance/Total time=240 km/7 hours
   
   Calculating this gives:
   Average speed=240km/7hrs ≈ 34.29 km/h
   
   So, the average speed for the entire journey is approximately 34.29 km/h

Hi Riddhi. 

I am Adithi. It's disappointing to work very hard for a certain goal and not get the result you deserve. But your 10th grades only show you marks, they cannot indicate your true capabilities. 
Keep going, keep learning. Become capable, become technically strong. Then, your marks will just become a byproduct. 
Just remember, becoming capable is the goal, not getting marks. 

Remember, you will struggle with JEE, regardless of your marks in 10th.

I can help you prepare in a smarter and more efficient manner to help with your stress. I am personally studying at NITK and know exactly what you are going through. Reach out to me anytime. Good luck!