Question

The area of a rhombus is 49 square millimeters. If one diagonal is twice as long as the other, what are the lengths of the diagonals?

Answer 1

The lengths of the diagonals are 7 mm and 14 mm

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

`A=(1)/(2)(xy)`

we have

`A=49\ mm^(2)`

so

`49=(1)/(2)(xy)`

`98=xy` -----> equation A

`x=2y` --------> equation B

substitute equatiin B in equation A and solve for y

`98=(2y)y\\98=2y^(2)\\y^(2)=49\\y=7\ mm`

Find the value of x

`x=2y`

`x=2(7)=14\ mm`

therefore

The lengths of the diagonals are 7 mm and 14 mm

Answer 2

Hello!

The answer is:

The lengths of the diagonals are:

`d_(1)=14mm`

`d_(2)=7mm`

Why?

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:

`d_(1)=2d_(2)`

`area=49mm^(2)`

We need to use the following formula

`Area=(d_(1)d_(2))/(2)`

Then,

Substituting and calculating we have:

`49mm^(2)=(2d_(2)d_(2))/(2)\\\\49mm^(2)=d_(2)^(2)\\\\\sqrt{49mm^(2)}=\sqrt{d_(2)^(2)}\\\\7mm=d_(2)`

We have that:

`d_(2)=7mm`

So, calculating the length of the diagonal 1, we have:

`d_(1)=2d_(2)`

`d_(1)=2*7mm=14mm`

Hence, we have that the answers are:

`d_(1)=14mm`

`d_(2)=7mm`

Have a nice day!