Beginning Algebra, 11th Edition

SECTION 2.5 Formulas and Additional Applications from Geometry^127

35. (volume of a pyramid); ,

36. ;,

37. (volume of a sphere);

38. ;

Solve each problem. See Examples 2 and 3.

39.The length of a rectangle is 9 in. more than the width. The perimeter is 54 in. Find the

length and the width of the rectangle.

40.The width of a rectangle is 3 ft less than the length. The perimeter is 62 ft. Find the length

and the width of the rectangle.

41.The perimeter of a rectangle is 36 m. The length is 2 m more than

three times the width. Find the length and the width of the

rectangle.

42.The perimeter of a rectangle is 36 yd. The width is 18 yd less

than twice the length. Find the length and the width of the

rectangle.

43.The longest side of a triangle is 3 in. longer than the short-

est side. The medium side is 2 in. longer than the shortest

side. If the perimeter of the triangle is 20 in., what are the

lengths of the three sides?

44.The perimeter of a triangle is 28 ft. The medium side is 4 ft longer than the shortest side,

while the longest side is twice as long as the shortest side. What are the lengths of the

three sides?

45.Two sides of a triangle have the same length. The third side measures 4 m less than twice

that length. The perimeter of the triangle is 24 m. Find the lengths of the three sides.

46.A triangle is such that its medium side is twice as long as its shortest side and its longest

side is 7 yd less than three times its shortest side. The perimeter of the triangle is 47 yd.

What are the lengths of the three sides?

Use a formula to solve each problem. (Use 3.14as an approximation for .) Formulas are

found on the inside covers of this book. See Examples 2– 4.

47.A prehistoric ceremonial site dating to

about 3000 B.C. was discovered in south-

western England. The site is a nearly per-

fect circle, consisting of nine concentric

rings that probably held upright wooden

posts. Around this timber temple is a

wide, encircling ditch enclosing an area

with a diameter of 443 ft. Find this en-

closed area to the nearest thousand square

feet. (Hint: Find the radius. Then use

.) (Source: Archaeology,vol. 51,

no. 1, Jan./Feb. 1998.)

a=pr^2

p

V= r= 6

4

3

pr^3

V= r= 12

4

3

pr^3

V= B= 36 h= 4

1

3

Bh

V= B= 12 h= 13

1

3

Bh

hh

r

3 W + 2

W

L

2 L – 18

443 ft

Reconstruction

Ditch

s + 3

s s + 2