Question

Draw a right triangle ABC in which AC = AB = 4.5 cm and ∠A = 90°. Draw a triangle similar to ΔABC with its sides equal to (5/4)^th of the corresponding sides of ΔABC.

Answer 1

Given that

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)^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 = 4.5cm.

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 = A₁A₂ = A₂A₃ = A₃A₄ = A₄A₅

Step: VII-Join A₄B.

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 A₅B' || 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.