Construct a , in which BC = 5cm, =60^ and altitude from A is equa… - Vidyadip

Question

Construct a $\triangle\text{ABC},$ in which BC = 5cm, $\angle\text{C}=60^\circ$ and altitude from A is equal to 3cm. Construct a $\triangle\text{ADE}$ similar to $\triangle\text{ABC},$ such that each side of $\triangle\text{ADE}$ is $\frac32$ times the corresponding side of $\triangle\text{ABC}$ Write the steps of construction.

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Answer

Step of constuction:

Draw a line segment BC = 5cm
Construct $\angle\text{BCP}=60^\circ$
Draw a line GH || BC at a distance of 3cm, intersecting CP at A.
Join AB and draw altitude $\text{AM}\perp\text{BC}.$ Thus, $\triangle\text{ABC}$ is obtained.
Extend AB to D such that $\text{AD}=\frac32\text{AB}.$
Draw DE || BC, cutting AC produced at E.

Then, $\triangle\text{ADE}$ is the required triangle similar to $\triangle\text{ABC}$ such that each side of $\triangle\text{ADE}$ is $\frac32\text{times}$ the corresponding side of $\triangle\text{ABC}$

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