In acute triangle ABC, AD⊥BC and DE⊥AB. Match the areas. List I List II (a) Area of triangle ADB. (P) ( b 2 /4)sin2C (b) Area of triangle ADC. (Q) ( c 2 /4) co s 2 B sin2B (c) Area of triangle ADE. (R

Question

In acute triangle ABC, AD⊥BC and DE⊥AB. Match the areas. List I List II (a) Area of triangle ADB. (P) ( b 2 /4)sin2C (b) Area of triangle ADC. (Q) ( c 2 /4) co s 2 B sin2B (c) Area of triangle ADE. (R) ( c 2 /4)sin2B (d) Area of triangle BDE. (S) ( c 2 /4) s i n 2 B sin2B

TestHub · Accepted Answer

Using right triangles ADB and ADE, Δ A D B =( c 2 /4)sin2B; Δ A D C =( b 2 /4)sin2C. Splitting ADB at E gives Δ A D E =( c 2 /4) s i n 2 B sin2B and Δ B D E =( c 2 /4) co s 2 B sin2B.

Mathematics - Properties of Triangle Question with Solution | TestHub

Options:

Doubts & Discussion

List I	List II
(a) Area of triangle ADB.	(P) ( $b^{2}$ /4)sin2C
(b) Area of triangle ADC.	(Q) ( $c^{2}$ /4) $co s^{2}$ B sin2B
(c) Area of triangle ADE.	(R) ( $c^{2}$ /4)sin2B
(d) Area of triangle BDE.	(S) ( $c^{2}$ /4) $s i n^{2}$ B sin2B