Draw a right triangleABCin whichAC=AB= 4.54 cm and∠A= 90°. Draw a triangle similar toΔABCwith its sides equal toth of th

Solution

Construct a right triangle of sides AC = AB = 4.5 cm and ∠A = 90° and then a triangle similar to it whose sides are (5/4)  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 = 4.5cm.

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

Step: III- With A as centre and radius AC = 4.5 cm

Step: IV- Join BC to obtain ΔABC.

Step: V- Below AB, makes an acute angle ∠BAX = 60°.

Step: VI- Along AX,  mark off five points A₁, A₂, A₃, A₄,  and A₅, such that AA₁ = A₁ A₂ = A₂ A₃ = A₃ A₄ = A₄ A₅

Step: VII-Join A₄ B.

Step: VIII- Since we have to construct a triangle each of whose sides is (5/4)^th of the corresponding sides of ΔABC.

So, we draw a line A₅B' on AX from point A₅  which is A₅ B' || A₄B, and meeting AB at B'.

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

Thus, ΔAB'C' is the required triangle, each of whose sides is (5/4)^th  of the corresponding sides of ΔABC.