Question

4. The perimeter of a rhombus is 560 meters and one of its diagonals has a length of 76 meters. Find the area of the rhombus. Part A: Determine the length of the other diagonal. Part B: The area is square meters.

Answer 1

Given

the perimeter of a rhombus is 560 meters

one of its diagonals has a length of 76 meters.

Procedure

The perimeter of a rhombus is:

P=4L

`\begin{gathered} P=4L \\ 560=4L \\ L=(560)/(4) \\ L=140 \end{gathered}`

if d1=76 and L=140, we can find d2

`\begin{gathered} ((d1)/(2))^2+((d2)/(2))^2=L^2 \\ ((76)/(2))^2+((d2)/(2))^2=140^2 \\ ((d2)/(2))^2=140^2-((76)/(2))^2 \\ (d2)/(2)^{}=√(19600-1444) \\ d2=269.48 \end{gathered}`

the area is:

`\begin{gathered} A=(d2\cdot d1)/(2) \\ A=(269.48\cdot76)/(2) \\ A=10240 \end{gathered}`

The answer is:

Part A: the length of the other diagonal is 269.48

Part B: The area is 10240 square meters.​