△ABC is a right angled triangle with ∠ABC = 90∘, AC = 13 cms and BC = 5 cm. BD is perpendicular to AC. If △BDC ~ △ABC, find the length of BD.
Here we are asked to find the length of the side BD. In order to measure the side we will start by constructing the triangle △ABC and then the similar triangle △BDC.
Steps of construction are as follows:
Step 1: Draw BC = 5 cm.
Step 2: Draw a line perpendicular to BC passing through B.
Step 3: Measure 13 cm length on a compass. With C as centre mark the length on the line perpendicular to BC at A.
Step 4: Join AC.
Now that we have got the triangle △ABC, we will start drawing the triangle BDC. Since △BDC ~ △ABC;
∠BDC = ∠ABC = 90∘, ∠C is common in both triangles and ∠BAC = ∠DBC.
Therefore if we draw a line passing through B, such that ∠BAC = ∠DBC.
Step 5: Draw a line passing through B, such that ∠BAC = ∠DBC, which intersects AC at D.
Now measure the length of the side BD. This should be equal to 4.6 cm.