Question

The number of squares that are required to fill a rectangle of 512 cm by 108 cm, if each square of length 8 cm is _____________. options a. 838 b. 864 c. 752 d. 440

Answer 1

✬ Square = 864 ✬

Step-by-step explanation:

Given:

• Measure of length and breadth of rectangle is 512 cm and 108 cm respectively.
• Length of each square is 8 cm.

To Find:

• How many squares will be required to fill the rectangle?

Solution: As we know that

★ Area of Rectangle = Length•Breadth ★

$\implies{\rm }$ Area = 512 $\times$ 108

$\implies{\rm }$ Area = 55296 cm²

Now, for square

★ Area of Square = Side² ★

$\implies{\rm }$ Area = 8²

$\implies{\rm }$ Area = 8 $\times$ 8

$\implies{\rm }$ Area = 64 cm²

∴ Total square required = Ar. Rectangle/Ar. square

➭ 55296/64

➭ 864 squares

Hence, 864 squares will be required to fill the rectangle. Option (B) is correct.

Answer 2

▪ Given -

• The number of squares that are required to fill a rectangle of 512cm by 108cm
• Length of each square tile is 8cm
• L = 512cm
• B = 108cm

▪ To Find -

• How many Squares are required to fill up the gap?

▪ Solution -

First of all, we have to find areas of square & rectangle to get Further Ans

☆ Area of Rectangle = Length × Breadth

Placing values according to conditions,

$⟹area \: of \: rectangle \: = length \: \times breadth$

$⟹a</strong><strong>r</strong><strong>e</strong><strong>a</strong><strong> = 512 \times 108$

$⟹a</strong><strong>r</strong><strong>e</strong><strong>a</strong><strong> = 55296 {cm}^{2}$

Now, Let's find area of Square,

☆ Area of Square = Side²

Placing Values according to Conditions,

$⟹area = {8}^{2}$

$⟹area = 64 {cm}^{2}$

Now, To find Length of tile, Formula will be -

☆ $length \: of \: tile \: = \frac{area \: of \: rectangle}{area \: of \: square}$

Placing Values,

$⟹length \: of \: tile \: = \frac{55296}{64}$

$⟹length \: of \: tile \: = \frac{\cancel{55296}}{\cancel{64}}$

$⟹length \: of \: tile \: = 864sq.cm$

⛬ Option B is correct