Answer:
9. MP = 49
10. VT = 62
Step-by-step explanation:
#9
∵ In the rhombus, all the sides are equal in length
∵ MNOP is a rhombus
∵ MN = NO = OP = PM
∵ MN = 9x - 77
∵ OP = 3x + 7
→ Equate them to find x
∴ 9x - 77 = 3x + 7
→ Add 77 to both sides
∴ 9x = 3x + 84
→ Subtract 3x from both sides
∴ 6x = 84
→ Divide both sides by 6
∴ x = 14
→ Substitute the value of x in the expression of OP to find its length
∵ OP = 3(14) + 7 = 42 + 7
∴ OP = 49
∵ All the sides are equal in length
∴ MP = 49
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#10
∵ The diagonals of the square bisect each other
∵ STUV is a square
∵ SU and TV are its diagonals
∴ W is the mid-point of SU and TV
∴ SW = WU
∵ SW = 2x + 13
∵ WU = 8x - 41
→ Equate them to find x
∴ 8x - 41 = 2x + 13
→ Add 41 to both sides
∴ 8x = 2x + 54
→ Subtract 2x from both sides
∴ 6x = 54
→ Divide both sides by 6
∴ x = 9
→ Substitute x in the expression of SW to find it
∵ SW = 2(9) + 13 = 18 + 13
∴ SW = 31
∵ SU = SW + WU
∵ SW = WU
∴ SU = 31 + 31 = 62
∵ Diagonals of the square are equal in length
∴ SU = VT
∴ VT = 62
