Question

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 5/3^th times the corresponding sides of the given triangle.

Answer 1

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 5/3^th 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 5/3^th 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 5/3^th of the corresponding sides of ΔABC.