Step-by-step explanation:

using the Pythagoras theorem in triangle BDC

BD =13 where base is 12 and perpendicular is 5

using Pythagoras theorem in triangle BAC

WHERE hypotenuse is 15 and base is 12

15²=12²+(AD+5)²

Ad comes out to be 56-10AD=AD²

hope it helps

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Verified answer

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In triangle ABC, Using Pythagoras theorem

AB²= AC²+BC²

AC²= AB²-BC²

= 15²- 12²

= 225-144

= 81

AC= √81= 9 cm

We know CD= 5 cm

Also, AC= CD+AD

AD= AC - CD

= 9-5= 4

AD= 4 cm.

Now, in Triangle BDC

BD² = BC² + CD²

= 12²+ 4²

= 144+ 16

BD²= 160

BD= √160

BD= 2√40 cm

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