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Constructions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsConstructions5 Marks
Question
Construct a $\triangle\text{ABC},$ in which $BC = 6.5\ cm$, $AB = 4.5\ cm$ and $\angle\text{ABC}=60^\circ.$
Construct a triangle similar to this triangle whose sides are $\frac{3}{4}$ the corresponding sides of $\triangle\text{ABC}.$
✓

Answer


Steps of Construction:
  1. Draw a line segment $BC = 6.5\ cm$
  2. At B, construct $\angle\text{CBX}=60^\circ$
  3. With B as center and radius $4.5\ cm$, draw an arc intersecting BX at A
  4. Join AC to obtain $\triangle\text{ABC}$
  5. Below BC, make an acute $\angle\text{CBY}$
  6. Along BY, mark off $4$ points $\Big($ greater of $3$ and in $\frac34\Big)$ $B_1, B_2, B_3, B_4$​​​​​​​ such that $BB_1 = B_1B_2 = B_2B_3 = B_3B_4$​​​​​​​
  7. Join $B_4C$
  8. From point $B_3$​​​​​​​, draw a line parallel to $B_4C$ intersecting $BC$ at $C'$
  9. From Point $C'$, draw a line parallel to $AC$ intersecting $AB$ at $A'$
Thus, $\triangle\text{A}'\text{BC}'$ is the required triangle.

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