Q. 14.1( 352 Votes )

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

Answer :

__Step 1:__ Draw line segment AB = 7.6 cm

__Step 2:__ Draw a ray AC making an acute angle with line segment AB .

__Step 3:__ Along AC, divide (5+8) 13 equals points

A_{1},A_{2},A_{3},……………….,A_{13} on AX such that

AA_{1}=AA_{2}=A_{2}A_{3} and so on .

__Step 4:__ Join BA_{13}

__Step 5:__ Through the point A_{5}, draw a line parallel to BA_{13} (by making an angle equal to ∠AA_{13}B) at A_{5} intersecting AB at point D.

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

The lengths of AD and DB 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 A_{5}D∥A_{13}B. By applying Basic proportionality theorem for

From the figure, it can be observed that AA_{5} and A_{5}A_{13} contain 5 and 8 equal divisions of line segments respectively.

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

This justifies the construction.

Rate this question :

Divide a line segment of length 9 cm internally in the ratio 4 : 3. Also, give justification of the construction.

RD Sharma - MathematicsDivide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

RD Sharma - MathematicsDraw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that .

RS Aggarwal - MathematicsIn Figure 4, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. (Use π = 3.14)

Mathematics - Board Papers

Draw a line segment AB of length 7 cm. Using ruler and compasses, find a point P on AB such that AP/AB = 3/5.

Mathematics - Board Papers