# In a right angle ΔABC, A = 90˚, AC = 8 and BC = 16. By considering AC

| In a right angle ΔABC, A = 90˚, AC = 8 and BC = 16. By considering AC as base an equilateral ΔACD is drawn. Find the maximum possible length of BD.

A. 8

B. 8

C. 16

D. None of these

### Right Answer is: A

#### SOLUTION

Equilateral ΔACD can be drawn on AC in two ways (i.e. downwards or upwards). But in order to find the maximum possible length of BD, we will draw it downwards.

Let us draw BEED

In ΔAED,

AD = 8 (All the sides of an equilateral triangle are equal)

EAD = 180˚ – 90˚ – 60˚ = 30˚

so AE = AD = 8 = 12

& ED = AD = 8 = 4

Now, in ΔABC,

AB^{2} = BC^{2} – AC^{2}

AB =

AB = 8

In ΔBED,

BD^{2} = BE^{2} + ED^{2}

BD^{2} = (8 + 12)^{2} + (4)^{2}

BD^{2} = 400 + 48

BD =

BD = 8

Share

In a right angle ΔABC, A = 90˚, AC = 8 and BC = 16. By considering AC