Answer:
AR = 24 units
RB = 25 units
Step-by-step explanation:
In a rectangle:
- Each two opposite sides are equal in length
- The two diagonals are equal in length
- The four angles are right angles
- The length of the diagonal is equal to the square root of the sum of the squares of its two dimensions
In rectangle ABCR
∵ AR and BC are opposite sides
∴ AR = BC
∵ AR = 3x + 6
∵ BC = x + 18
- Equate them to find x
∴ 3x + 6 = x + 18
- Subtract x from both sides
∴ 2x + 6 = 18
- Subtract 6 from both sides
∴ 2x = 12
- Divide both sides by 2
∴ x = 6
Substitute the value of x in the expression of AR to find its length
∵ AR = 3(6) + 6
∴ AR = 18 + 6
∴ AR = 24 units
∵ AC is a diagonal of rectangle ABCR
∴ [tex]AC=\sqrt{(AR)^{2}+(RC)^{2}}[/tex]
∵ AR = 24 units
∵ RC = 7 units
∴ [tex]AC=\sqrt{(24)^{2}+(7)^{2}}=\sqrt{576+49}=\sqrt{625}[/tex]
∴ AC = 25 units
∵ RB is a diagonal of the rectangle ABCR
∵ The two diagonal of the rectangle are equal in length
∴ AC = RB
∴ RB = 25 units
