NCERT solution Class 10 constructions

NCERT Solutions

Class 10 Maths

Constructions

NCERT Questions

Ex.11.1 Q.1
Ex.11.1 Q.2
Ex.11.1 Q.3
Ex.11.1 Q.4
Ex.11.1 Q.5
Ex.11.1 Q.6
Ex.11.1 Q.7
Ex.11.2 Q.1
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5
Ex.11.2 Q.6
Ex.11.2 Q.7

Ex.11.1 Q.1

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

Measure the two parts. Give the justification of the construction.

A line segment of length 7.6 cm can be divided in the ratio of 5: 8 as follows:

Step 1. Draw line segment AB of 7.6 cm and draw a ray AX making an acute angle with line segment AB.

Step 2. Locate 13 (= 5 + 8) points, A₁, A₂, A₃, A₄ ,........, A₁₃ on AX such that AA₁ = A₁ A₂ = A₂ A₃ and so on.

Step 3. Join BA₁₃.

Step 4. Through the point A₅, draw a line parallel to BA₁₃ (by making an angle equal to ∠AA₁₃ B) at A₅ intersecting AB at point C.

Now, C is the point dividing line segment AB of 7.6 cm in the required ratio of 5: 8.

The lengths of AC and CB can be measured. It comes out to 2.9 cm and 4.7 cm respectively.

Justification:

The construction can be justified by proving that

By construction, we have A₅ C || A₁₃ B.

By applying Basic proportionality theorem for the triangle AA₁₃ B, we obtain

= AA₅ ÷ A₅ A₁₃ …………... (1)

From the figure, it can be observed that AA₅ and A₅A₁₃ contain 5 and 8 equal divisions of line segments respectively.

AA₅ ÷ A₅ A₁₃ = ……….... (2)

On comparing equations (1) and (2), we obtain

This justifies the construction.

Video solution:

Constructions Class 10 Maths NCERT Chapter 11 NCERT Solutions

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NCERT solutions of Constructions Class 10 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 10 Maths Constructions NCERT solutions.