Question

2) Selena is planning a patio that will adjoin the sides of her L-shaped home. One side of the patio is 24 ft. And the other is 18 ft.The shape of the patio is triangular. Draw a representation of the patio and find the area if the length of the third side is 30 ft.

Answer 1

Explanation:

GIVEN: Selena is planning a patio that will adjoin the sides of her L-shaped home. One side of the patio is
`24\text{ feet}`. And the other is
`18\text{ feet}`.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
`30\text{ feet}`.

SOLUTION:

Consider the figure attached.

one of triangular patio
`=18\text{ feet}`

other of triangular patio
`=24\text{ feet}`

as third side of patio is of length
`30\text{ feet}`

as, sides of patio forms a Pythagorean triplet

`18^2+24^2=30^2`

Therefore, there is right angle between sides of length
`18\text{ feet}` and
`24\text{ feet}`.

area of patio
`=(1)/(2)* base * height`

`(1)/(2)*24*18`

`=216\text{ feet}^2`

Hence the area of triangular patio is
`216\text{ feet}^2`