Question

Work must be shown for this problem! The figure shown below is a rhombus. Remember to solve for x and then find NO! Give both answers below!

Answer 1

x = 6

NO = 26

Explanation:

recall that for a rhombus all the sides are of equal length,

which means, PM = MN = MP = NO

we are given

MP = 5x-4 and MN = 6x-10

since MP = MN, thus

5x-4 = 6x-10 (add 4 to both sides)

5x = 6x - 10 + 4

5x = 6x - 6 (subtract 6x from both sides)

5x-6x = -6

-x = -6

x = 6 (answer)

NO = MP = 5x-4 = 5(6) - 4 = 30 - 4 = 26

Answer 2

x=6

NO=26

Explanation:

MP=5x-4, MN=6x-10

Since it is a rhombus, all sides are congruent, thus MP is congruent to MN

and:

5x-4=6x-10

6x-10=5x-4

6x=5x+6

x=6

So, MP=5(6)-4=30-4=26, since all sides of a rhombus are congruent, MP=NO

26=PO

NO=26