The answer is:
The lengths of the diagonals are:
[tex]d_{1}=14mm[/tex]
[tex]d_{2}=7mm[/tex]
To solve the problem, we need to use the formula to calculate the area of a rhombus involving its diagonals and create a relation between the diagonals of the given rhombus.
So, from the statement we know that:
[tex]d_{1}=2d_{2}[/tex]
[tex]area=49mm^{2}[/tex]
We need to use the following formula
[tex]Area=\frac{d_{1}d_{2}}{2}[/tex]
Then,
Substituting and calculating we have:
[tex]49mm^{2}=\frac{2d_{2}d_{2}}{2}\\\\49mm^{2}=d_{2}^{2}\\\\\sqrt{49mm^{2}}=\sqrt{d_{2}^{2}}\\\\7mm=d_{2}[/tex]
We have that:
[tex]d_{2}=7mm[/tex]
So, calculating the length of the diagonal 1, we have:
[tex]d_{1}=2d_{2}[/tex]
[tex]d_{1}=2*7mm=14mm[/tex]
Hence, we have that the answers are:
[tex]d_{1}=14mm[/tex]
[tex]d_{2}=7mm[/tex]
Have a nice day!
Answer:
The lengths of the diagonals are 7 mm and 14 mm
Step-by-step explanation:
we know that
To find the area of a rhombus, multiply the lengths of the two diagonals and divide by 2
Let
x-------> the length of one diagonal
y -----> gthe length of the another diagonal
The area of a rhombus is equal to
[tex]A=\frac{1}{2}(xy)[/tex]
we have
[tex]A=49\ mm^{2}[/tex]
so
[tex]49=\frac{1}{2}(xy)[/tex]
[tex]98=xy[/tex] -----> equation A
[tex]x=2y[/tex] --------> equation B
substitute equatiin B in equation A and solve for y
[tex]98=(2y)y\\98=2y^{2}\\y^{2}=49\\y=7\ mm[/tex]
Find the value of x
[tex]x=2y[/tex]
[tex]x=2(7)=14\ mm[/tex]
therefore
The lengths of the diagonals are 7 mm and 14 mm
