Advertisements
Advertisements
Question
In figure, ∠ABC = 90°, AD = 15 cm and DC = 20 cm. If BD is the bisector of ∠ABC, then perimeter of ΔABC is ______.
Fill in the Blanks
Advertisements
Solution
In figure, ∠ABC = 90°, AD = 15 cm and DC = 20 cm. If BD is the bisector of ∠ABC, then perimeter of ΔABC is 84 cm.
Explanation:
By the Angle Bisector Theorem, `(AD)/(DC) = (AB)/(BC)`.
So `(AB)/(BC) = 15/20 = 3/4`.
Let AB = 3k and BC = 4k.
Then AC = AD + DC
= 15 + 20
= 35
= 5k
So k = 7.
Thus AB = 21 cm, BC = 28 cm, AC = 35 cm.
Perimeter = 21 + 28 + 35
= 84 cm
shaalaa.com
Is there an error in this question or solution?
