Question

$△ABC$ is a right angled triangle with $\angle ABC$ = 90${}^{\circ }$, AC = 13 cms and BC = 5 cm. BD is perpendicular to AC. If $△BDC$ ~ $△ABC$, find the length of BD.

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Answer 1

Here we are asked to find the length of the side BD. In order to measure the side we will start the 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 $△BDC$ ~ $△ABC$;

$\angle BDC$ = $\angle ABC$ = 90${}^{\circ }$, $\angle C$ is common in both triangles and $\angle BAC$ = $\angle DBC$.

Therefore if we draw a line passing through B, such that $\angle BAC$ = $\angle DBC$.

Step 5: Draw a line passing through B, such that $\angle BAC$ = $\angle DBC$, which intersects AC at D.

Now measure the length of the side BD. This should be equal to 4.6 cm.