Home/Class 10 Math Chapter List/10. Constructions/# Draw a line segment of length (7.6;cm) and divide it in the ratio (5:8.)Measure the two parts.

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

see the solution below

To Keep Reading This Answer, Download the App

4.6

Review from Google Play

4.6

Review from Google Play

To Keep Reading This Answer, Download the App

Steps of construction·

1.Draw a line segment\(AB=7.6\;cm\)

2.Draw a ray \(AX,\)making an acute \(\angle BAX\).

3. Along\(AX,\). mark\(5+8=13\)points \(A_{1},A_{2},A_{3},A_{4},\cdots ,A_{12},A_{13}\)such that

\(AA_{1}=A_{1}A_{2}=A_{2}A_{3}=A_{3}A_{4}=A_{4}A_{5}=A_{5}A_{6}=A_{6}A_{7}\)\(=A_{7}A_{8}=A_{8}A_{9}=A_{9}A_{10}=A_{10}A_{11}=A_{11}A_{12}=A_{12}A_{13}\)

4. Join\(A_{13}B.\)

5. From\(A_{5}\)draw\(A_{5}O|| A_{13}B\) meeting \(AB\) at \(O\). [By making an angle equal to \(\angle AA_{13}B]\)

Then, \(O\) is the point on AB which divides it in the ratio \(5:8\).

So,\(AO:OB=5:8\)

Justification

Let \(AA_{1}=A_{1}A_{2}=A_{2}A_{3}=A_{3}A_{4}=A_{4}A_{5}\)

\(=A_{5}A_{6}=A_{5}A_{7}=\cdots =A_{12}A_{13}=x\)

\(\Delta ABA_{13},\)we have

\(A_{5}O|| A_{13}B\)

\(\therefore \frac {AO}{OB}=\frac {AA_{5}}{A_{5}A_{13}}=\frac {5x}{8x}=\frac {5}{8}\) (By basic proportionality theorem)

Hence,\(AO:OB=5:8\)

On measuring, we find that\(AO=2.9\;cm\)

and \(OB=4.7\;cm\)

1.Draw a line segment\(AB=7.6\;cm\)

2.Draw a ray \(AX,\)making an acute \(\angle BAX\).

3. Along\(AX,\). mark\(5+8=13\)points \(A_{1},A_{2},A_{3},A_{4},\cdots ,A_{12},A_{13}\)such that

\(AA_{1}=A_{1}A_{2}=A_{2}A_{3}=A_{3}A_{4}=A_{4}A_{5}=A_{5}A_{6}=A_{6}A_{7}\)\(=A_{7}A_{8}=A_{8}A_{9}=A_{9}A_{10}=A_{10}A_{11}=A_{11}A_{12}=A_{12}A_{13}\)

4. Join\(A_{13}B.\)

5. From\(A_{5}\)draw\(A_{5}O|| A_{13}B\) meeting \(AB\) at \(O\). [By making an angle equal to \(\angle AA_{13}B]\)

Then, \(O\) is the point on AB which divides it in the ratio \(5:8\).

So,\(AO:OB=5:8\)

Justification

Let \(AA_{1}=A_{1}A_{2}=A_{2}A_{3}=A_{3}A_{4}=A_{4}A_{5}\)

\(=A_{5}A_{6}=A_{5}A_{7}=\cdots =A_{12}A_{13}=x\)

\(\Delta ABA_{13},\)we have

\(A_{5}O|| A_{13}B\)

\(\therefore \frac {AO}{OB}=\frac {AA_{5}}{A_{5}A_{13}}=\frac {5x}{8x}=\frac {5}{8}\) (By basic proportionality theorem)

Hence,\(AO:OB=5:8\)

On measuring, we find that\(AO=2.9\;cm\)

and \(OB=4.7\;cm\)

To Keep Reading This Answer, Download the App

4.6

Review from Google Play

4.6

Review from Google Play

To Keep Reading This Answer, Download the App

Correct41

Incorrect0

Still Have Question?

Load More

More Solution Recommended For You