in a right-angled triangle,base =12cm hypotenuse is 15cm find the prependicular
pls answer it fast pls
Answers
Answer:
Right Angled Triangle. NOT TO SCALE
Fact: Base (length “ b “) is 12cm.
Fact: Hypotenuse (length “ c “) is 13cm.
Fact: Height (length" a “) is not known.
Task: Find the area of the triangle.
Analysis
The area of a triangle is half the length of the base multiplied by the height.
To find the height, we need to use Pythagorus' Theorem.
Pythagorus
Referring to the triangle shown in Sketch (1) above:
( a^2 ) + ( b^2 ) = ( c^2 ) so
The Hypotenuse = c = sqrt[ ( a^2 ) + ( b^2 ) ] or
( 13 ) = sqrt[ ( 12^2 ) + ( Height^2 ) ]
Squaring both sides of the equation:
( 169 ) = ( 144 ) + ( Height^2 ) so
( Height ) = sqrt( 25 )
Therefore ( Height ) = +/- ( 5 )
We cannot (obviously) have a negative height on a triangle so the true height of this triangle is +5cm.
Area of the Triangle
Area = ( 1/2 ) * (Base of Triangle ) * (Height of Triangle ).
or
= ( 0.5 ) * ( 12 ) * ( 5 ) or
= ( 30 )cm^2