Question : Asha and Suman's mud forts have heights of 9 cm and 16 cm. They are 24 cm apart. How far (in cm) are the fort tops from each other?
Option 1: 25
Option 2: 24
Option 3: 7
Option 4: 16
Correct Answer: 25
Solution : Height of Asha's mud fort = AB = 9 cm Height of Suman's mud fort = DE = 16 cm Distance between mud forts = BD = 24 cm AB = CD AC = BD From the above figure, DE = CD + CE ⇒ DE = AB + CE ⇒ CE = DE – AB ⇒ CE = 16 – 9 ⇒ CE = 7 cm In ΔACE, By using Pythagoras theorem, $(\text{AE})^2 = (\text{AC})^2 + (\text{CE})^2$ ⇒ $(\text{AE})^2$ = (24)2 + (7)2 ⇒ $(\text{AE})^2$ = 576 + 49 ⇒ $(\text{AE})^2$ = 625 ⇒ AE = $\sqrt{625} $ ⇒ AE = 25 cm $\therefore$ The fort tops are 25 cm far from each other. Hence, the correct answer is 25 cm.
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Question : Asha and Suman's mud forts have 9 cm and 16 cm heights. If the fort tops are 25 cm apart from each other, then the distance (in cm) between the two forts is:
Option 1: 24
Option 2: 16
Option 3: 25
Option 4: 7
Question : The average height of three kids is 56 cm and their heights are in the proportions of 7 : 8 : 9. Find the heights of all three.
Option 1: 42 cm, 48 cm, and 54 cm
Option 2: 56 cm, 64 cm, and 72 cm
Option 3: 35 cm, 40 cm, and 45 cm
Option 4: 49 cm, 56 cm, and 63 cm
Question : Two circles with radii of 25 cm and 9 cm touch each other externally. The length of the direct common tangent is:
Option 1: 34 cm
Option 2: 30 cm
Option 3: 36 cm
Option 4: 32 cm
Question : Points 'A' and 'B' are 70 km apart on a highway. A car starts from 'A' and another from 'B' at the same time. If they travel in the same direction, they meet in 7 hours, but if they travel towards each other, they meet in one hour. Find the speed of the two cars (in km/hr).
Option 1: 20, 30
Option 2: 40, 30
Option 3: 30, 50
Option 4: 20, 40
Question : The radii of two circles are 5 cm and 3 cm. The distance between their centre is 24 cm. Then the length of the transverse common tangent is:
Option 1: $16$ cm
Option 2: $15\sqrt{2}$ cm
Option 3: $16\sqrt{2}$ cm
Option 4: $15$ cm
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