Question

in rhombus ABCD the measure in inches of AB is 3x+2 and BC is x+12 Find the number of inches in the length of DC

Answer 1

In a rhombus, all sides are equal in length, so the lengths of AB and DC must be the same. By setting the expressions for AB and BC equal to each other and solving for x, we find that the length of DC is 17 inches.

Step-by-step explanation:

In a rhombus, all sides are of equal length. Therefore, if the length of AB is given as 3x + 2 and the length of BC is given as x + 12, since AB and BC are sides of the same rhombus, their lengths must be equal. To find the value of x, we set 3x + 2 equal to x + 12 and solve for x:

• 3x + 2 = x + 12
• 2x = 10
• x = 5

The length of DC, which is equal to the length of AB in a rhombus, is therefore 3(5) + 2 = 15 + 2 = 17 inches. So, DC measures 17 inches.

Answer 2

Answer: 17 inches

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Rule: All four sides of a rhombus are the same length

So AB = BC

Use this to solve for x

AB = BC

3x+2 = x+12

3x-x = 12-2

2x = 10

x = 5

If x = 5, then

AB = 3*x+2 = 3*5+2 = 15+2 = 17

and

BC = x+12 = 5+12 = 17

Both sides are 17 as expected, so the proper x value is confirmed.

So DC is also 17 since AB = DC