Question

In a triangle ABC $a=7,b=8,c=9$ BD is the median and BE is the altitude from the vertex B then

List-I	List-II
A) BD	1. 7
B) BE	2. 2
C) ED	3. $\sqrt{35}$
	4. $\sqrt{45}$

The correct match for LIST-I FROM LIST-II

• A. A-2, B-1, C-4
• B. A-3, B-4, C-2
• C. A-1, B-3, C-2
• D. A-1, B-4, C-2

Answer 1

The correct option is D A-1, B-4, C-2

$cosA=\frac{b^2+c^2-a^2}{2bc}$
$=\frac{8^2+9^2-7^2}{2\times 8\times 9}$
$=\frac{2}{3}$
$\frac{2}{3}=\frac{4^2+9^2-d^2}{2\times 4\times 3}$
$d^2=49$
$d=7$
$\frac{1}{2}\times 8\times 9\times sinA=\frac{1}{2}\times 8\times 4$
$4=\frac{39\times \sqrt{3^2-4^2}}{3}$
$h=\sqrt{45}$
$ED=\sqrt{d^2-h^2}$
$=\sqrt{49-45}$
$=2$