Mensuration
- If the length of the diagonal AC of a square ABCD is 5.2 cm, then the area of the square is :
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Using Rule 10,
Side of square = Diagonal √2 ∴ Area = (Diagonal)² 2 = (5.2)² = 27.04 = 13.52cm² 2 2 Correct Option: B
Using Rule 10,
Side of square = Diagonal √2 ∴ Area = (Diagonal)² 2 = (5.2)² = 27.04 = 13.52cm² 2 2
- The diagonal of a square is 4√2 cm. The diagonal of another square whose area is double that of the first square is :
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Using Rule 10, Side of the first square
= 1 × 4√2 = 4cm √2
Its area = (4)² = 16 cm².
∴ Area of second square = 2 × 16 = 32 cm².
Its side = √32 = 4 √2cm.
∴ Required diagonal = √2 × 4√2 = 8 cmCorrect Option: D
Using Rule 10, Side of the first square
= 1 × 4√2 = 4cm √2
Its area = (4)² = 16 cm².
∴ Area of second square = 2 × 16 = 32 cm².
Its side = √32 = 4 √2cm.
∴ Required diagonal = √2 × 4√2 = 8 cm
- The diagonal of a square A is (a+b). The diagonal of a square whose area is twice the area of square A, is
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Using Rule 10,
Area of the square A = (diagonal)² 2 = (a + b)² 2 Area of the new square = (a + b)² × 2 = (a + b)² 2
⇒ Side = (a + b)
∴ Diagonal = √2 × side = √2 (a + b)Correct Option: C
Using Rule 10,
Area of the square A = (diagonal)² 2 = (a + b)² 2 Area of the new square = (a + b)² × 2 = (a + b)² 2
⇒ Side = (a + b)
∴ Diagonal = √2 × side = √2 (a + b)
- The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq.cm. Find the length of the greater line segment if one is longer than the other by 2 cm.
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Let the length of the smaller line segment = x cm.
The length of larger line segment = (x + 2) cm.
According to the question,
(x + 2)² – x² = 32
⇒ x² + 4x + 4 – x² = 32
⇒ 4x = 32 – 4 = 28⇒ x = 28 = 7 4
The required length = x + 2 = 7 + 2 = 9 cm.Correct Option: B
Let the length of the smaller line segment = x cm.
The length of larger line segment = (x + 2) cm.
According to the question,
(x + 2)² – x² = 32
⇒ x² + 4x + 4 – x² = 32
⇒ 4x = 32 – 4 = 28⇒ x = 28 = 7 4
The required length = x + 2 = 7 + 2 = 9 cm.
- The ratio of the area of a square to that of the square drawn on its diagonal is :
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Using Rule 10, Let the side of square be a units. Area of this square = a²
The diagonal of square = √2a
∴ Area of square = 2a²
∴ Required ratio = a² : 2a²
= 1 : 2Correct Option: B
Using Rule 10, Let the side of square be a units. Area of this square = a²
The diagonal of square = √2a
∴ Area of square = 2a²
∴ Required ratio = a² : 2a²
= 1 : 2
