Area Questions and Answers

• 29. The sides of a triangle are in the ratio of \begin{aligned}\frac{1}{2}:\frac{1}{3}:\frac{1}{4}\end{aligned}. If the perimeter is 52 cm, then find the length of the smallest side.

  1. 12 cm
  2. 14 cm
  3. 16 cm
  4. 18 cm

  Answer :

  Option A

  Explanation:

  \begin{aligned}
  \text{Ratio of sides =}\frac{1}{2}:\frac{1}{3}:\frac{1}{4} \\
  =6:4:3\\
  Perimeter = 52 cm \\
  \text{So sides are =} \\
  \left( 52*\frac{6}{13}\right)cm,\left( 52*\frac{4}{13}\right)cm, \left( 52*\frac{3}{13}\right)cm
  \end{aligned}
  a = 24 cm, b = 16 cm and c = 12 cm
  Length of the smallest side = 12 cm
  

• 30. The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .

  1. 22 cm
  2. 24 cm
  3. 26 cm
  4. 28 cm

  Answer :

  Option B

  Explanation:

  We know perimeter of square = 4(side)
  So Side of first square = 40/4 = 10 cm
  Side of second square = 32/4 = 8 cm
  
  Area of third Square = 10*10 - 8*8
  = 36 cm
  
  So side of third square = 6 [because area of square = side*side]
  Perimeter = 4*Side = 4*6 = 24 cm