Math, asked by DiyaPMishra, 7 months ago

16. The width of a rectangle is two-thirds its length. If the perimeter is 180 metres, find the
dimensions of the rectangle.
17. An altitude of a triangle is five-thirds the length of its corresponding base. If the altitude be
increased by 4 cm and the base decreased by 2 cm, the area of the triangle remains the
same. Find the base and the altitude of the triangle.
18. Two angles of a triangle are in the ratio 4:5. If the sum of these angles is equal to the third
angle, find the angles of the triangle.
19. A steamer goes downstream from one port to another in 9 hours. It covers the same
distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the
steamer in still water and the distance between the ports.
20. The distance between two stations is 300 km. Two motorcyclists start simultaneously from
these stations and move towards each other. The speed of one of them is 7 km/h more than
that of the other. If the distance between them after 2 hours of their start is 34 km, find the
speed of each motorcyclist. Check your solution.
21. Divide 150 into three parts such that the second number is five-sixths the first and the third
number is four-fifths the second.
22. Divide 4500 into two parts such that 5% of the first part is equal to 10% of the second part.
23. Rakhi's mother is four times as old as Rakhi. After 5 years, her mother will be three times
as old as she will be then. Find their present ages.
24. Monu's father is 26 years younger than Monu's grandfather and 29 years older than Monu.
The sum of the ages of all the three is 135 years. What is the age of each one of them?
25. A man is 10 times older than his grandson. He is also 54 years older than him. Find their
present ages.
26. The difference between the ages of two cousins is 10 years. 15 years ago, if the elder one was
twice as old as the younger one, find their present ages.
27. Half of a herd of deer are grazing in the field and three-fourths of the remaining are playing
nearby. The rest 9 are drinking water from the pond. Find the number of deer in the herd.
Hint. Let the number of deer in the herd be x.
Number of those who are grazing
х
2
Remaining -
2.
Number of those who are playing
3 x
4 2
3x
* 3x
+
2 8
8
+9=x. Find x.

Answers

Answered by BrainlyKingdom

Let Length of Rectangle be x, then Width of the Rectangle = ⅔ x

We know : Perimeter of Rectangle is 2 × (Length + Breadth)

⇒ 180 m = 2 × (x + ⅔ x)

⇒ 180 m = 2x + 2 × (⅔ x)

⇒ 180 m = 2x + ⁴⁄₃ x

⇒ 180 m = ⁶⁄₃ x + ⁴⁄₃ x

⇒ 180 m = ⁶⁺⁴⁄₃ x

⇒ 180 m = ¹⁰⁄₃ x

⇒ 180 m × 3 = 10x

⇒ 540 m = 10x

⇒ 54 m = x

Therefore

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