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# Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts

**Solution:**

- Draw the line segment of the given length.
- Then draw another line that makes an acute angle with the given line.
- Divide the line into m + n parts where m and n are the ratios given.
- The basic proportionality theorem states that “If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally".

Steps of construction:

- Draw AB = 7.6 cm
- Draw ray AX, making an acute angle with AB
- Mark 13 (i.e, 5 + 8) points as A₁, A
_{₂},….A_{₁₃}on AX such that AA_{₁}= A_{₁}A_{₂}= A_{₂}A_{₃}=...... A_{₁₂}A_{₁₃} - Join BA
_{₁₃} - Through A
_{₅}(since we need 5 parts to 8 parts) draw CA_{₅}parallel to BA_{₁₃}where C lies on AB.

Now AC: CB = 5 : 8

By measurement, we find that AC = 2.9 cm and CB = 4.7 cm

Proof:

CA_{₅} is parallel to BA_{₁₃}

By Basic Proportionality theorem, in ΔAA_{₁₃}B

AC/BC = AA_{₅}/A_{₅}A_{₁₃} = 5/8 (By Construction)

Thus, C divides AB in the ratio 5:8.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 11

**Video Solution:**

## Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts

NCERT Solutions Class ₁0 Maths Chapter 11 Exercise 11.1 Question 1

**Summary:**

Point C divides the line segment AB of length 7.6 cm in the ratio of 5:8. By measurement, we find that AC = 2.9 cm and CB = 4.7 cm.

**☛ Related Questions:**

- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are 2/3 of the corresponding sides of the first triangle.
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of the first triangle.
- Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are 1(1/2) times the corresponding sides of the isosceles triangle.
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/2 of the corresponding sides of the triangle ABC.

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