Question

Draw a line segment of length 7.5 cm and divide it in the ratio 3:8. Write the steps of construction​

Answer 1

Step-by-step explanation:

Step-1 Draw a line segment AB=7.5 cm

According to the question-

2x+3x=7.5 cm

x=1.5

Step-2 Mark 5 arcs of equal length of 1.5 cm

Hence,

AC=2×1.5⇒3.0 cm

BC=3×1.5⇒4.5 cm.

Hence, this is the answer.

Answer 2

The construction (Diagram) of a line segment of length 7.5 cm in the ratio of 3:8 is in the attachment below. FC divides AB at C in the ratio  AC: CB = 3:8.

Given:

We have to divide a line segment AB = 7.5 cm in the ratio 3: 8 internally.

Steps of construction:

To divide a given line segment into parts having a given ratio :

Step 1. Draw a line segment AB = 7.5 cm and then draw a ray AX  making an acute angle to AB.

Step 2. Divide AX into as many equal parts as the sum of the terms of the ratio.

Here the sum of ratio is 3 + 8 = 11. Therefore, divide AX into 11 equal parts at D, E, F, G, H, I, J …. N.

Step 3. Join NB. Draw FC || NB from the third point of division F. Then FC divides AB at C in the ratio 3: 8 internally, i.e., AC: CB = 3:8.

Hence, FC divides AB at C in the ratio  AC: CB = 3:8.

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