Question

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Answer 1

Answer:

BD = 7.5 cm

Step-by-step explanation:

We are given,

AC = 15 cm

∠ B = 90°

AD = CD

BD ⊥ AC

Now,

In ΔABD and ΔCBD,

AD = CD (Side)

∠ADB = ∠CDB = 90° [BD ⊥ AC] (Angle)

BD = BD [Common side] (Side)

∴ ΔABD ≅ ΔCBD [By SAS congruency]

Thus,

∠ABD = ∠CBD [Corresponding parts of Congruent Triangles]

Now,

∠B = 90°

∠B = ∠ABD + ∠CBD

90° = ∠ABD + ∠ABD

90° = 2∠ABD

∠ABD = 90/2

∠ABD = 45°

Now,

we are given,

AD = CD

Also,

AC = AD + CD

AC = AD + AD

AC = 2AD

Given, AC = 15 cm

15 = 2AD

AD = 15/2

AD = 7.5 cm

Now, we must use Trigonometry,

Tan 45° = AD/BD

Tan 45° = 1

Thus,

1 = AD/BD

BD = AD

AD = 7.5 cm

∴ BD = 7.5 cm

Hope it helped and believing you understood it........All the best