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Question
Draw a right triangle in which sides (other than the hypotenuse) are of lengths 8 cm and 6 cm. Then construct another triangle whose sides are 3/4 times the corresponding sides of the first triangle.
Solution
Given that
Construct a right triangle of sides let AB = 8cm, AC = 6cm and ∠ A = 90° and then a triangle similar to it whose sides are 3/4th 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 let AB = 8cm.
Step: II- With A as centre and draw an angle ∠ A = 90°.
Step: III- With A as centre and radius AC = 6cm.
Step: IV-Join BC to obtain right ΔABC.
Step: V- Below AB, makes an acute angle ∠BAX = 60°.
Step: VI- Along AX, mark off five points A1, A2, A3 and A4 such that AA1 = A1A2 = A2A3 = A3A4
Step: VII- Join A4B.
Step: VIII -Since we have to construct a triangle each of whose sides is 3/4th of the corresponding sides of right ΔABC.
So, we draw a line A3B' on AX from point A3 which is A3B' || 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 3/4th of the corresponding sides of ΔABC.
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