Answer:
BD = 14
Step-by-step explanation:
Using Pythagoras' identity on Δ's ADC and ABC
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, thus
BC² + 12² = 15²
BC² + 144 = 225 ( subtract 144 from both sides )
BC² = 81 ( take the square root of both sides )
BC = [tex]\sqrt{81}[/tex] = 9
and
DC² + 12² = 13²
DC² + 144 = 169 ( subtract 144 from both sides )
DC² = 25 ( take the square root of both sides )
DC = [tex]\sqrt{25}[/tex] = 5
Hence
BD = BC + DC = 9 + 5 = 14
