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