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

Answer:

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

Step-by-step explanation:

Diagonals of rhombus bisect each at 90 degree angle.

In rhombus ABCD

OA = OC =$\frac{24 feet}{2}= 12 feet$

OB = OD = $\frac{18 feet}{2}= 9 feet$

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.

Answer 2

One side of the fenced-in garden is 15 ft