20. In a triangle ABC, perpendicular AD from A on BC meets BC at D. If BD = 8cm,
DC = 2cm and AD = 4cm, then
a) triangle ABC is isosceles
b) triangle ABC is equilateral
C) AC = 2AB
d) triangle ABC is right - angled at A.
Answers
Answered by
11
Given: -
- In ΔABC, point D lies on BC such that AD is perpendicular to BC.
- BD = 8 cm,
- DC = 2 cm,
- AD = 4 cm.
ΔADC is a right-angled triangle, therefore use Pythagoras' theorem.
AC² = AD² + DC²
= 4 ² + 2 ²
= 20 ......... (1)
Similarly, in ΔADB,
AB² = AD² + BD²
= 4² + 8²
= 80 .......... (2)
In ΔABC, we use Pythagoras' theorem to see that
BC² = AB² + AC²
= 80 + 20 (using values in Equations (1) and (2))
BC = 10 .......... (3)
This value of BC coincides with the given value of BC (= BD + DC = 10 cm) .
Therefore, ΔABC is a right-angled triangle, by the converse of Pythagoras' theorem.(OPTION D)
____________________________
Answered by
1
Answer:
4th and 3rd of the following is equal to my current
Similar questions