SOLUTION: I would appreciate if a tutor would teach me how to solve the following word problems step by step. 1) Solve the problem. The height of a box is 8 inches. The length is th

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Question 87191: I would appreciate if a tutor would teach me how to solve the following word problems step by step.
1) Solve the problem.
The height of a box is 8 inches. The length is three inches more than the width. Find the width if the volume is 560.
Question 3 answers
8 in.
10 in.
70 in.
7 in.
2) Solve the problem.
A square lawn has an area of 1568 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?
Question 4 answers
39.6 feet
28 feet
56 feet
19.8 feet
3) Answer the question.
If a rectangle is x feet long and y feet wide, which one of the following expressions is the length of its diagonal in terms of x and y?
Question 5 answers
x2 + y2
x + y
square root x+y
square root x^2 + y^2
4) Solve the problem.
The area of a square is numerically 117 more than the perimeter. Find the length of the side.
Question 6 answers
85 units
52 units
13 units
338 units

Found 2 solutions by checkley75, stanbon:
Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
1) HEIGHT=8 INCHES, LENGTH=W+3 INCHES, WIDTH=W.
VOLUME =L*W*H
560=(W+3)*W*8
560=(W^2+3W)*8
560/8=W^2+3W
70=W^2+3W
W^2+3W-70=0
(W+10)(W-7)=0
W+10=0
W=-10 NOT AN ANSWER.
W-7=0
W=7 ANSWER.
PROOF
560=(7+3)*7*8
560=10*7*8
560=560
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2) 1568=S^2
S=SQRT1568
S=39.597979 IS THE LENGTH OF THE SIDES.
THUS THE RADIUS IS S/2
39.597979/2=19.798989 FEET.
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3) SQRT(X^2+Y^2)
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4)AREA=S^2 & PERIMETER=4S. THUS:
S^2=4S+117
S^2-4S-117=0
(S-13)(S+9)=0
S-13=0
S=13 ANSWER.
PROOF
13^2=4*13+117
169=52+117
169=169

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
1) Solve the problem.
The height of a box is 8 inches. The length is three inches more than the width. Find the width if the volume is 560.
----------
Let width be x; length = x+3
Volume = width*length*height
560 = x(x+3)*8
70 = x^2+3x
x^2+3x-70=0
(x+10(x-7)=0
x=7 inches (width)
x+3=10 inches (length)
=========================
2) Solve the problem.
A square lawn has an area of 1568 square feet. A sprinkler placed at the center of the lawn sprays a water in a circular pattern that just covers the lawn. What is the radius of the circle?
Area = pi(r^2)
1568 = pi(r^2)
r^2 = 1568/pi
r = 22.34 ft.
================
3) Answer the question.
If a rectangle is x feet long and y feet wide, which one of the following expressions is the length of its diagonal in terms of x and y?
Question 5 answers
Answer: square root (x^2 + y^2)
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4) Solve the problem.
The area of a square is numerically 117 more than the perimeter. Find the length of the side.
Perimeter = 4s
Area = s^2
Area = 4s+117
s^2-4s-117 = 0
(s-13)(x+9)=0
Answer: s = 13 units
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Cheers,
Stan H.