Question

hi pls answer it
Q9 ​

Answer 1

~Answer :

• 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.

$~$

${\sf:\implies{\dfrac{1}{2}~×~AD~×~BC}}$

${\sf:\implies{\dfrac{1}{\cancel{2}}~×~6~×~\cancel{16}}}$

${\sf:\implies{8~×~6}}$

• ${\underline{\boxed{\pmb{\sf{\pink{48 cm^2}}}}}} \; {\red{\bigstar}}$

$~$

Now, area with base AC & height BE,

$~$

${\sf:\implies{48~=~\dfrac{1}{2}~×~BE~×~AC}}$

${\sf:\implies{48~=~\dfrac{1}{\cancel{2}}~×~BE~×~\cancel{12}}}$

${\sf:\implies{48~=~BE~×~6}}$

${\sf:\implies{BE~=~\cancel\dfrac{48}{6}}}$

• ${\underline{\boxed{\pmb{\sf{\purple{BE~=~8 cm}}}}}} \; {\red{\bigstar}}$

$~$

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

$~$

${\sf:\implies{48~=~\dfrac{1}{2}~×~AB~×~h}}$

${\sf:\implies{48~=~\dfrac{1}{\cancel{2}}~×~\cancel{10}~×~h}}$

${\sf:\implies{48~=~5~×~h}}$

${\sf:\implies{h~=~\cancel\dfrac{48}{5}}}$

• ${\underline{\boxed{\pmb{\sf{\pink{h~=~9.6 cm}}}}}} \; {\red{\bigstar}}$

$~$

Hence,

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