Question

Draw a right triangle in which sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then, construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle. [CBSE 2011]

Answer 1

Steps of Construction

Step 1. Draw a line segment BC = 3 cm.

Step 2. At B, draw $\angle$XBC = 90º.

Step 3. With B as centre and radius 4 cm, draw an arc cutting BX at A.

Step 4. Join AC. Thus, a right ∆ABC is obtained.

Step 5. Extend BC to D such that BD = $\frac{5}{3}$BC = $\frac{5}{3}\times 3$ cm = 5 cm.

Step 6. Draw DE || CA, cutting BX in E.



Here, ∆BDE is the required triangle similar to ∆ABC such that each side of ∆BDE is $\frac{5}{3}$ times the corresponding side of ∆ABC.