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.

Answer 1

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 3/4^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 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 3/4^th 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 3/4^th of the corresponding sides of ΔABC.