Question

in the figure , in triangle ABC , BC=16cm , AC=12cm , AB=10cm and altitude AD =6cm . Find a)BE b)altitude on side AB​

Answer 1

Answer:

56 I yjink mmm...,..............

Answer 2

The value of BE is 8 cm and altitude on side AB is 9.6 cm.

Given :

• BC = 16 cm
• AC = 12 cm
• AB = 10 cm
• altitude AD = 6 cm

To Find :

• The value of BE and altitude on side AB ?

______________

Solution :

• Area of triangle with height AD & base BC.

${\sf:\implies{\dfrac{1}{2}~×~AD~×~BC}} \\{\sf:\implies{\dfrac{1}{\cancel{2}}~×~6~×~\cancel{16}}} \\{\sf:\implies{8~×~6}} \\{\underline{\boxed{\pmb{\sf{\green{48 cm^2}}}}}} \; {\blue{\bigstar}}$

Now, area with base AC & height BE,

${\sf:\implies{48~=~\dfrac{1}{2}~×~BE~×~AC}} \\ {\sf\implies{48~=~\dfrac{1}{\cancel{2}}~×~BE~×~\cancel{12}}} \\{\sf:\implies{48~=~BE~×~6}}\\{\sf: \implies{BE~=~\cancel\dfrac{48}{6}}} \\ {\underline{\boxed{\pmb{\sf{\green{BE~=~8 cm}}}}}} \;{\blue{\bigstar}}$

• Area of triangle with altitude on side AB is given by ;

${\sf:\implies{48~=~\dfrac{1}{2}~×~AB~×~h}} \\{\sf:\implies{48~=~\dfrac{1}{\cancel{2}}~×~\cancel{10}~×~h}} \\{\sf:\implies{48~=~5~×~h}} \\{\sf:\implies{h~=~\cancel\dfrac{48}{5}}} \\ {\underline{\boxed{\pmb{\sf{\green{h~=~9.6 cm}}}}}} \; {\blue{\bigstar}}$

Hence,

• The value of BE is 8 cm and altitude on side AB is 9.6 cm.