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Here's your question..
Word Problem:-
Meena has a square piece of cloth of area 125 cm². She wants to know whether she can make a handkerchief of side 15 cm. If that is not possible she wants to know what is the maximum length of the side of a handkerchief that can be made from the piece.
Chapter:- Squares and Square Roots.
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Answers
Given:
- Meena has a square piece of cloth of area 125 cm².
- She wants to know whether she can make a handkerchief of side 15 cm.
To find:
- The maximum length of the side of a handkerchief that can be made from the piece?
Solution:
⠀⠀⌬ Let length of the square be s.
Now,
According to the given Question:
☆ Area of square = 125 cm²
⇏ side × side = 125
⇏ (Side)² = 125
⇏ Side = √125
⇏ 5√5 ≈ 15cm
- Side of the handkerchief cannot be 15cm. As, the Area would be, (15)² = 225 cm.
∴ Hence, maximum length of the side of a handkerchief that can be made from the piece is 5√5.
⠀⠀⠀━━━━━━━━━━━━━━━━━━
⠀⠀⠀⠀★ Formulas related to it :
- Perimeter of square = 4 × side
- Area of Square = side × side
- Diagonal of square = √2 a
Given :- Meena has a square piece of cloth of area 125 cm². She wants to know whether she can make a handkerchief of side 15 cm.
To Find :- If that is not possible she wants to know what is the maximum length of the side of a handkerchief that can be made from the piece.
Answer :-
→ Total cloth area = 125 cm².
and,
→ if meena would have make a handkerchief of side 15cm, then area of handkerchief = (side)² = (15)² = 225 cm².
since,
→ Total cloth area < area of handkerchief .
→ 125 < 225 .
therefore, it is not possible to make a handkerchief of side 15 cm.
now, Let maximum length of side is a cm .
so,
→ a² ≤ 125
→ a ≤ √(125)
→ a ≤ √(5 * 5 * 5)
→ a ≤ 5√5
therefore, maximum length of a is 5√5 cm .
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