Mensuration
- The area of two equilateral triangles are in the ratio 25 : 36. Their altitudes will be in the ratio :
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The ratio of the area of two similar triangles is equal to the ratio of square of the corresponding altitudes.
Ratio of altitudes = √25 = 5 √36 6
or 5 : 6Correct Option: C
The ratio of the area of two similar triangles is equal to the ratio of square of the corresponding altitudes.
Ratio of altitudes = √25 = 5 √36 6
or 5 : 6
- ABC is an equilateral triangle of side 2 cm. With A, B, C as centre and radius 1 cm three arcs are drawn. The area of the region within the triangle bounded by the three arcs is
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Using Rule 17,
Each angle of the triangle = 60°
Required area of the three sectors= 3 × 60 × π(i)² 360 = π cm² 2 Area of triangle = √3 × 4 = √3cm² 4 ∴ Required area = 
√3 - π 
cm² 2 Correct Option: C
Using Rule 17,
Each angle of the triangle = 60°
Required area of the three sectors= 3 × 60 × π(i)² 360 = π cm² 2 Area of triangle = √3 × 4 = √3cm² 4 ∴ Required area = √3 - π cm² 2
- The area of a right-angled isosceles triangle having hypotenuse 16√2 cm is
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Using Rule 1,
Let AB = BC = x;
AC = 16√2
∴ x² + x² = (16√2)²
⇒ 2x² = 16 × 16 × 2
⇒ x² = 16 × 16
⇒ x = 16∴ Area of triangle = 1 × base × height 2 = 1 × 16 × 16 = 128cm² 2 Correct Option: B
Using Rule 1,
Let AB = BC = x;
AC = 16√2
∴ x² + x² = (16√2)²
⇒ 2x² = 16 × 16 × 2
⇒ x² = 16 × 16
⇒ x = 16∴ Area of triangle = 1 × base × height 2 = 1 × 16 × 16 = 128cm² 2
- The sides of a triangle are in the ratio 2 : 3 : 4. The perimeter of the triangle is 18 cm. The area (in cm2) of the triangle is
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Using Rule 2 and 3,
Ratio = 2 : 3 : 4
= 4 : 6 : 8 Perimeter = 18 cm∴ Semi-perimeters = 4 + 6 + 8 = 9 2
∴ Area of triangle = √s(s - a)(s - b)(s -c)
= √9(9 - 4)(9 - 6)(9 - 8)
= √9 × 5 × 3 × 1
= 3√15sq.cm.Correct Option: D
Using Rule 2 and 3,
Ratio = 2 : 3 : 4
= 4 : 6 : 8 Perimeter = 18 cm∴ Semi-perimeters = 4 + 6 + 8 = 9 2
∴ Area of triangle = √s(s - a)(s - b)(s -c)
= √9(9 - 4)(9 - 6)(9 - 8)
= √9 × 5 × 3 × 1
= 3√15sq.cm.
- If the numerical value of the perimeter of an equilateral triangle is 3 times the area of it, then the length of each side of the triangle is
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Using Rule 6,
If the side of the equilateral triangle be x units, then,3x =√3 √3 x² 4 ⇒ 3x = 3x² 4
⇒ x = 4 unitsCorrect Option: C
Using Rule 6,
If the side of the equilateral triangle be x units, then,3x =√3 √3 x² 4 ⇒ 3x = 3x² 4
⇒ x = 4 units
