Mathematics, 29.01.2020 18:55 luckyalita

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?

Answers: 3

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Answer from: meadowsoares7

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

$Area=\frac{d_{1}d_{2}}{2}$

Then,

Substituting and calculating we have:

$49mm^{2}=\frac{2d_{2}d_{2}}{2}\\\\49mm^{2}=d_{2}^{2}\\\\\sqrt{49mm^{2}}=\sqrt{d_{2}^{2}}\\\\7mm=d_{2}$

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!

Answer from: lordicy

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

$A=\frac{1}{2}(xy)$

we have

$A=49\ mm^{2}$

$49=\frac{1}{2}(xy)$

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 from: Quest

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step-by-step explanation:

Answer from: Quest

let's solve your equation step-by-step.

4x+2=2x+12

step 1: subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

step 2: subtract 2 from both sides.

2x+2−2=12−2

2x=10

step 3: divide both sides by 2.

x=5

step-by-step explanation:

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The area of a rhombus is 49 square millimeters. if one diagonal is twice as long as the other, what...

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