Question

Timothy has a fenced-in garden in the shape of a rhombus. The length of the longer diagonal is 24 feet, and the length of the shorter diagonal is 18 feet.

What is the length of one side of the fenced-in garden?

12 ft
15 ft
21 ft
108 ft

Answer 1

One side of the fenced-in garden is 15 ft

Answer 2

15 feet is the length of one side of the fenced-in garden.

Explanation:

Diagonals of rhombus bisect each at 90 degree angle.

In rhombus ABCD

OA = OC =
`(24 feet)/(2)= 12 feet`

OB = OD =
`(18 feet)/(2)= 9 feet`

Since, the diagonal intersect at 90 degree angle.

Applying Pythagoras theorem in ΔAOB

`OA^2+OB^2=AB^2`

`(12 feet)^2+(8 feet)^2=AB^2`

AB = 15 feet = Length of side of the rhombus fenced garden

15 feet is the length of one side of the fenced-in garden.