Answer:
Step-by-step explanation:
GIVEN: Selena is planning a patio that will adjoin the sides of her L-shaped home. One side of the patio is [tex]24\text{ feet}[/tex]. And the other is [tex]18\text{ feet}[/tex].The shape of the patio is triangular.
TO FIND: Draw a representation of the patio and find the area if the length of the third side is [tex]30\text{ feet}[/tex].
SOLUTION:
Consider the figure attached.
one of triangular patio [tex]=18\text{ feet}[/tex]
other of triangular patio [tex]=24\text{ feet}[/tex]
as third side of patio is of length [tex]30\text{ feet}[/tex]
as, sides of patio forms a Pythagorean triplet
[tex]18^2+24^2=30^2[/tex]
Therefore, there is right angle between sides of length [tex]18\text{ feet}[/tex] and [tex]24\text{ feet}[/tex].
area of patio [tex]=\frac{1}{2}\times base \times height[/tex]
[tex]\frac{1}{2}\times24\times18[/tex]
[tex]=216\text{ feet}^2[/tex]
Hence the area of triangular patio is [tex]216\text{ feet}^2[/tex]
