Question

Angle A = 90 , AD perpendicular to BC . If BD = 2 cm and CD = 8 cm, find AD.

Answer 1

Please see the attachment

Answer 2

Answer:

The length of AD = 4

Step-by-step explanation:

Given,

∠A = 90°

AD is perpendicular to BC

BD = 2cm and CD = 8cm

To find,

The length of AD

Recall the theorem

Pythagoras Theorem

In a right-angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

Solution:

Since ∠A = 90°, ΔABC is a right-angled triangle.

Then by Pythagoras theorem,

BC² = AB² + AC² -------------------(1)

We have BC = BD +CD

since BD = 2cm and CD = 8cm

BC = 10cm

(1) becomes,

AB² + AC² = 10² = 100

AB² + AC² = 100--------------(2)

Again, since AD is perpendicular to BC, Triangles ADB and ADC are right-angled triangles

Then by Pythagoras theorem, we have,

AB² = BD² + AD²

and AC² = CD² + AD²

Substitute the value of AB²  and AC² in equation(2) we get

BD² + AD² +  CD² + AD² = 100

2² + AD² +  8² + AD²  = 100

4+64 +2AD²  = 100

68 +2AD²  = 100

2AD² = 100 - 68 = 32

AD² = 16

AD = 4

∴The length of AD = 4cm

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