Question

Please help me with this problem:

the base of a rectangle is 9/4 of the height and the perimeter is 104 dm. Calculate the perimeter of the square equivalent to four times the rectangle​

Answer 1

`\boxed{384}`

Explanation:

• Let B be the base of the rectangle and H the height

• We are given
  
  `B = (9)/(4)H`

• Perimeter is given by 2(B+H) = 104

• So
  
  `B + H = (104)/(2) = 52`
  

• 
  `\textrm{Substitute }B = (9)/(4)H`,
  
  `(9)/(4)H + H = 52`

• Multiply throughout by 4:
  
  `4 \cdot (9)/(4)H + 4H = 4 \cdot 52\\\\\\9H + 4H = 208\\\\13H = 208\\\\H = (208)/(13) = 16\\\\B = (9)/(4)H = (9)/(4)\cdot 16 = 36\\\\\\`

• Area of this rectangle = 16 x 36 = 576

• If we have a square that is the same size of this rectangle, then it's area should also be 576

• Since the area of a square of side a is a² and if a² = 576,
  
  `a = \displaystyle √(576) = 24`

• So each side of a square that is equivalent to the rectangle would be 24

• A square four times this size would have a side = 4 x 24 = 96

• The perimeter of a square of side
  `a` is
  `4a`

• So the perimeter of the square equivalent to four times the rectangle​ would be
  4 x 96 = 384