Draw a right triangle in which the sides (other than hypotenuse) are of lengths 5 cm and 4 cm. Then construct another triangle whose sides are 5/3th times the corresponding sides of the given triangle.
Solution
Given that
Construct a right triangle of sides let AB = 5cm, AC = 4cm and ∠A = 90° and then a triangle similar to it whose sides are 5/3th of the corresponding sides of .
We follow the following steps to construct the given
Step of construction
Step: I- First of all we draw a line segment AB = 5cm.
Step: II- With A as centre and draw an angle ∠A = 90°.
Step: III- With A as centre and radius AC = 4cm.
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 A3B.
Step: VIII -Since we have to construct a triangle each of whose sides is 5/3th of the corresponding sides of ΔABC.
So, we draw a line A5B on AX from point A5 which is A5B' || A3B, 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 5/3th of the corresponding sides of ΔABC.
