Chapter 4, Problem 15CST

(a)

To determine

To find: The three possible length of the squares.

Answer to Problem 15CST

3 cm, 6 cm, 9 cm

Explanation of Solution

Given: A wooden board that measures 54 cm by 90 cm. Use all wood and cut identical squares pieces with integer side lengths.

First take scale of wooden block.

Let scale 18 cm = 1 mm

So, the ratio of the sides of the wooden block 3:5

Now find the HCF of 54 and 90 i,e 18

All the factors of 18 will give exactly square block from wooden board.

Three possible length of square will be factors of 18.

If choose the length of square be 3 cm, 6 cm and 9 cm.

(b)

To determine

To find:The largest side length of the square.

Answer to Problem 15CST

  $18\text{ cm}$

Explanation of Solution

Given: A wooden board that measures 54 cm by 90 cm. Use all wood and cut identical squares pieces with integer side lengths.

First take scale of wooden block.

Let scale 18 cm = 1 mm

So, the ratio of the sides of the wooden block 3:5

Now find the HCF of 54 and 90 i,e 18

If choose largest side length of the square is 18. The board used perfectly.

No wastage of wood.

Because the dimension of wooden board is multiple of 18. It is Highest common multiple of 54 and 90.

(C)

To determine

To find: The number of square pieces if side length of square is 18 cm.

Answer to Problem 15CST

  $15$

Explanation of Solution

Given: A wooden board that measures 54 cm by 90 cm. Use all wood and cut identical squares pieces with integer side lengths.

The side length of square is 18 cm.

Number square cut from wooden board.

Along length, Total square cut $=\frac{90}{18}=5$

Along width, Total square cut $=\frac{54}{18}=3$

Therefore, the total number of square cut whose side length 18 cm will be 15.