Question

Draw a right triangle in which the sides (other than the hypotenuse) are of lengths 4 cm and 3 cm. Now construct another triangle whose sides are `3/5` times the corresponding sides of the given triangle.

Answer 1

Construct a right triangle of sides AB = 4 cm, AC = 3 cm and ∠A = 90° and then a triangle similar to it whose sides are `(3/5)^"th"` of the corresponding sides of ΔABC

We follow the following steps to construct the given

Step of construction

Step: I- First of all we draw a line segment AB = 4 cm.

Step: II- With A as centre and draw an angle ∠A = 90°.

Step: III- With A as centre and radius AC = 3 cm.

Step: IV-Join BC to obtain right ΔABC.

Step: V- Below AB, makes an acute angle ∠BAX.

Step: VI- Along AX, mark off five points A₁, A₂, A₃, A₄ and A₅ such that =A₄A₅.

Step: VII- Join A₅B.

Step: VIII -Since we have to construct a triangle each of whose sides is (`3/5`)th of the corresponding sides of right ΔABC

So, we draw a line on AX from point which is A₃B ∥ A₅B and meeting AB at B’.

Step: IX- From B’ point draw B'C' || BCand meeting AC at C’

Thus, ΔABC is the required triangle, each of whose sides is `(3/5)`th of the corresponding sides of ΔABC.