8Number 8ExplanationA cuboid-shaped cardboard box has a base perimeter of 6x cm6x \text{ cm}6x cm and a height of (5−13x) cm\left(5 - \frac{1}{3}x\right) \text{ cm}(5−31x) cm where xxx is a real number. If the width of the box's base is (4x−5) cm(4x - 5) \text{ cm}(4x−5) cm, the length of the base is ... cm.x−5x - 5x−5x+5x + 5x+55−x5 - x5−x5−2x5 - 2x5−2x2x−52x - 52x−5ExplanationWe will find the length of the cuboid's base using the formula for the perimeter of a rectangle. Using the Base Perimeter Formula The base of the box is rectangular, so its perimeter formula (KKK) is: K=2(p+l)K = 2(p + l)K=2(p+l) Given: Base perimeter (KKK) = 6x6x6x Base width (lll) = 4x−54x - 54x−5 We substitute these values into the formula: 6x=2(p+(4x−5))6x = 2(p + (4x - 5))6x=2(p+(4x−5)) Calculating Base Length We simplify the equation to solve for ppp. Divide both sides by 2: 6x2=p+4x−5\frac{6x}{2} = p + 4x - 526x=p+4x−53x=p+4x−53x = p + 4x - 53x=p+4x−5 Rearrange the terms to isolate ppp: p=3x−4x+5p = 3x - 4x + 5p=3x−4x+5p=−x+5p = -x + 5p=−x+5p=5−xp = 5 - xp=5−x So, the length of the box's base is (5−x) cm(5 - x) \text{ cm}(5−x) cm.
