Mensuration
- Which of the following ratios can be the ratio of the sides of a right angled triangle?
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In a right angled triangle,
Perpendicular² = base² + perpendicular²
13² = 12² + 5² = 144 + 25 = 169
⇒ 13 : 12 : 5Correct Option: B
In a right angled triangle,
Perpendicular² = base² + perpendicular²
13² = 12² + 5² = 144 + 25 = 169
⇒ 13 : 12 : 5
- PS is a diameter of a circle of radius 6 cm. In the diameter PS, Q and R are two points such that PQ, QR and RS are all equal. Semicircles are drawn on PQ and QS as diameter (as shown in the figure). The perimeter of shaded portion is :
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PQ = QR = RS = 2 cm.
Perimeter of shaded region = QS + PS + PQ
= π × 2 + π × 1 + π × 3= 6π = 6 × 22 = 132 = 18 6 cm. 7 7 7 Correct Option: D
PQ = QR = RS = 2 cm.
Perimeter of shaded region = QS + PS + PQ
= π × 2 + π × 1 + π × 3= 6π = 6 × 22 = 132 = 18 6 cm. 7 7 7
- The perimeter of a certain isosceles right triangle is 10 + 10√2 cm. What is the length of the hypotenuse of the triangle ?
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AB = BC = x cm.
∴ AC = √AB² + BC²
= √x² + x² = √2x² = 2x cm.
∴ AB + BC + CA = 10 + 10√2
⇒ 2x + √2x = 10 + 10√2
⇒ √2x (√2 + 1) = 10(1 + √2)
⇒ √2x = 10 cm. = ACCorrect Option: B
AB = BC = x cm.
∴ AC = √AB² + BC²
= √x² + x² = √2x² = 2x cm.
∴ AB + BC + CA = 10 + 10√2
⇒ 2x + √2x = 10 + 10√2
⇒ √2x (√2 + 1) = 10(1 + √2)
⇒ √2x = 10 cm. = AC
- The radius of wheel moving on a road, is
8 3 cm 4
How many rounds it will take to complete 55 metre distance.
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Distance covered by wheel in one revolution = Circumference of wheel = 2πr
= 2 × 22 × 35 = 55 cm. 7 4 ∴ Required number of revolutions = 55 × 100 = 100 55 Correct Option: C
Distance covered by wheel in one revolution = Circumference of wheel = 2πr
= 2 × 22 × 35 = 55 cm. 7 4 ∴ Required number of revolutions = 55 × 100 = 100 55
- The sides of a triangle are in the ratio
1 : 1 : 1 2 3 4
and its perimeter is 104 cm. The length of the longest side (in cm) is
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Ratio of the sides of triangle = 1 : 1 : 1 2 3 4 = 1 × 12 : 1 × 12 : 1 × 12 = 6 : 4 : 3 2 3 4
Sum of the terms of ratio = 6 + 4 + 3 = 13∴ Largest side = 
6 × 104 
cm. 13
= 48 cm.Correct Option: B
Ratio of the sides of triangle = 1 : 1 : 1 2 3 4 = 1 × 12 : 1 × 12 : 1 × 12 = 6 : 4 : 3 2 3 4
Sum of the terms of ratio = 6 + 4 + 3 = 13∴ Largest side = 6 × 104 cm. 13
= 48 cm.
