Question

A metal plate measuring $32$ cm by $12$ cm is cut up into the small squares of side length $4$ cm. How many squares will be cut?

Answer 1

Hint: First find the area of the metal plate and then find the area of the square. After that, use them to find the number of squares.

Complete step by step solution:
It is given that the measurement of the metal plate is $32$ cm by $12$ cm. Then find the area of the metal plate using the given data. There is a formula for the area of a rectangle because the plate has a rectangular shape. The formula is given as:
${\text{Area of the rectangular plate}} = {\text{length}} \times {\text{width}}$
Find the area of the plate by the substitution of $32$ for length and $12$ for width in the above formula.
${\text{Area of the rectangular plate}} = 32 \times 12$
${\text{Area of the rectangular plate}} = 384{\text{ c}}{{\text{m}}^2}$
Therefore, the area of the rectangular plate having measurement $32$ cm by $12$ cm is$384{\text{ c}}{{\text{m}}^2}$.

It is also given that the side length of the square is $4{\text{ cm}}$. Now, find the area of the square using the formula:
${\text{Area of the square}} = {\left( {{\text{side}}} \right)^2}$
Substitute the value of the side as $4{\text{ c}}{{\text{m}}^2}$ in the above equation to find the area of the square.
${\text{Area of the square}} = {\left( 4 \right)^2}$
${\text{Area of the square}} = 16{\text{ c}}{{\text{m}}^2}$
The goal is to find the number of square pieces that can be cut from the given rectangular plate.
Use the formula given below:
${\text{Number of pieces = }}\dfrac{{{\text{Area of rectangular plate}}}}{{{\text{Area of one square plate}}}}$
Substitute the area of the rectangular plate $384{\text{ c}}{{\text{m}}^2}$and the area of the square piece $16{\text{ c}}{{\text{m}}^2}$to get the number of pieces.
${\text{Number of pieces = }}\dfrac{{{\text{384}}}}{{16}}$
${\text{Number of pieces = }}24$

Therefore, 24 pieces of a square can be cut from the rectangular plate.

Note: It is a must notice that the unit of both the dimensions of the metal plate and the dimension of the small square will have to be the same. If the units are different then the answer has gone to be wrong.