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Constructions — Maths STD 10 — Question

Maharashtra BoardEnglish MediumSTD 10MathsConstructions4 Marks
Question
Construct a $\triangle\text{ABC}$ in which AB = 5cm, $\angle\text{B} = 60^\circ,$ altitude $CD = 3cm.$ Construct a $\triangle\text{AQR}$ similar to $\triangle\text{ABC}$ such that side of $\triangle\text{AQR}$ is 1.5 times that of the corresponding sides of $\triangle\text{ABC}.$
✓

Answer

Steps of construction:
  1. Draw a line segment $AB = 5cm.$
  2. At A, draw a perpendicular and cut off $AE = 3cm.$
  3. From E, draw $EF || AB.$
  4. From B, draw a ray making an angle of 60 meeting $EF$ at $C.$
  5. Join $CA$. Then ABC is the triangle.
  6. From A, draw a ray AX making an acute angle with AB and cut off 3 equal parts making $AA_1 = A_1A_2 = A_2A_3.$
  7. Join $A_2$ and $B.$
  8. From $A,$ draw $A'B’$ parallel to $A_2B$ and $B’C’$ parallel to $BC.$
Then $\triangle\text{C}'\text{AB}'$ is the required triangle.

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