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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.
Solution
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.
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