**
**

**Respect Responsibility
Readiness**

8. The length of a rectangle is 3 times the width. If the length is decreased by 4 m and the width is increased by 1 m, the perimeter will be 66 m. Find the dimensions of the original rectangle.

9. The length of a rectangle is 6 cm longer than the width. If the length is increased by 9 cm and the width by 5cm, the perimeter will be 160 cm. Find the dimensions of the original rectangle.

10. The length of a rectangle is 7 m less than twice the width. If the length is decreased by 1 m and the width by 4 m, the perimeter will be 66 m. Find the dimensions of the original rectangle.

11. The perimeter of a
triangle is 69 cm. Side ** a** is 5 cm shorter than side

12. The first side of a triangle is 7 cm shorter than twice the second side. The third side is 4 cm longer than the first side. The perimeter is 80 cm. Find the length of each side.

13. The length of a rectangular field is 18 m longer than the width. The field is enclosed with fencing and divided into two parts with a fence parallel to the shorter sides. If 216 m of fencing are required, what are the dimensions of the outside rectangle? (See diagram to the right.)

14. The length of a
rectangle is 3 cm greater than the width. If each dimension is increased by 2
cm, the area is increased by 26 cm^{2}. Find the original dimensions of
the rectangle.

15. The length of a
rectangle is 2 cm greater than the width. If the width is increased by 3 cm, and
the length is increased by 4 cm, the area is increased by 88 cm^{2}.
Find the original dimensions of the rectangle.

16. A rectangular garden is
4 m longer than it is wide. If the width is decreased by 1 m, and the length is
increased by 5 m, the area is increased by 15 m^{2}. Find the original
dimensions of the garden.

17. A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Find the original dimensions of the pool.

18. A rectangular picture
is 6 cm longer than it is wide. A frame 1 cm wide is placed around the picture.
The area covered by the picture and frame together is 48 cm^{2 }greater
than the area of the picture alone. Find the dimensions of the picture.

19. The length of a
rectangle is 3 cm more than the width. The area is 70 cm^{2}. Find the
dimensions of the rectangle.

20. The length of a
rectangle is 4 cm more than the width. The area is 96 cm^{2}. Find the
dimensions of the rectangle.

21. The length of a
photograph is 1 cm less than twice the width. The area is 45 cm^{2}.
Find the dimensions of the photograph.

22. If the sides of a
square are increased by 3 m, the area becomes 64 m^{2}. Find the length
of a side of the original square.

23. A square field had 5 m
added to its length and 2 m added to its width. The field then had an area of
130 m^{2}. Find the length of a side of the original held.

24. The dimensions of a
rectangular garden were 4 m by 5 m. Each dimension was increased by the same
amount. The garden then had an area of 56 m^{2}. Find the dimensions of
the new garden. (Hint: Let x be the amount of increase.)

25. The dimensions of a rectangular garden were 3 m by 10 m. When both dimensions were increased by equal amounts, the area of the garden doubled. Find the dimensions of the new garden.

26. A 4 m by 6 m rug covers half of the floor area of a room and leaves a uniform strip of bare floor around the edges. What are the dimensions of the room?

27. The length of a
rectangle is 4 m more than the width. The area of the rectangle is 45 m^{2}.
Find the length and width.

28. The length of a
rectangle is three times the width. The area is 108 cm^{2}. Find the
dimensions of the rectangle.

29. The length of a
photograph is 1 cm less than twice the width. The area is 28 cm^{2}.
Find the dimensions of the photograph.

30. A square field had 3 m
added to its length and 2 m added to its width. The field then had an area of 90
m^{2}. Find the length of a side of the original field.

31. The length of a
rectangular mural is 2 m greater than the width. The area is 20 m^{2}.
Find the dimensions of the mural.

32. The length of a
rectangle is 6 cm more than the width. The area is 11 cm^{2}. Find the
length and width.

33. The length of a
rectangular garden is 4 m greater than the width. The area is 71 m^{2}.
Find the dimensions of the garden.

34. The length of a
rectangular park is 2 km less than twice the width. The area is 9 km^{2}.
Find the dimensions of the park.

35. The base of a triangle
is 3 cm longer than its altitude. The area of the triangle is 35 cm^{2}.
Find the altitude. (Hint: The area of a triangle equals ˝ base•altitude.)

36. The altitude of a
triangle is 2 cm shorter than its base. The area is 15 cm^{2}. Find the
base of the triangle.

37. A flower garden is in
the shape of a right triangle. The longest side of the triangle measures 13 m.
One of the shorter sides is 7 m longer than the other. Find the length of the
shortest side. (Hint: Use the Pythagorean Theorem: a^{2 }+ b^{2 =
}c^{2}.) The diagonal measure of a movie screen is 6 m. The length
of the screen is 2 m greater than the height. Find the dimensions of the screen.

38. A square picture is mounted in a frame 1 cm wide. The area of the picture is of the total area. Find the length of a side of the picture.

39. A rectangular pond
measures 3 m by 5 m. A concrete walk of uniform width is constructed around the
pond. If the walk and pond together cover an area of 39 m^{2}, how wide
is the walk?

40. A rectangular counter is covered with 600 square tiles. The counter could have been covered with 400 tiles 1 cm longer on a side. Find the length of a side of the smaller tile.

41. The length of a rectangle is 5 m greater than the width. The perimeter is 150 m. Find the width and length.