Questions: Consider the following word problem: Consider a square and a regular hexagon (a six-sided figure with sides of equal length). One side of the square is 19 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure? Length of one side of the square: feet Length of one side of the hexagon: feet

Consider the following word problem: Consider a square and a regular hexagon (a six-sided figure with sides of equal length). One side of the square is 19 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure? Length of one side of the square: feet Length of one side of the hexagon: feet
Transcript text: Consider the following word problem: Consider a square and a regular hexagon (a six-sided figure with sides of equal length). One side of the square is 19 feet longer than a side of the hexagon, and the two figures have the same perimeter. What are the lengths of the sides of each figure? Step 2 of 2: Use the equations to solve the given problem. Answer How to enter your answer (opens in new window) Keypad Keyboard Shortcuts Previous Part Answer Length of one side of the square: $\square$ feet Length of one side of the hexagon: $\square$ feet Tutor Skip Try Similar Submit Answer 11:42 PM $8 / 31 / 2024$
failed

Solution

failed
failed

Solution Steps

To solve this problem, we need to set up equations based on the given conditions. Let \( s \) be the side length of the hexagon. The side length of the square is then \( s + 19 \). The perimeter of the hexagon is \( 6s \) and the perimeter of the square is \( 4(s + 19) \). Since the perimeters are equal, we can set up the equation \( 6s = 4(s + 19) \) and solve for \( s \). Once we find \( s \), we can easily find the side length of the square.

Step 1: Define Variables and Set Up the Equation

Let \( s \) be the side length of the hexagon. The side length of the square is \( s + 19 \). The perimeter of the hexagon is \( 6s \) and the perimeter of the square is \( 4(s + 19) \). Since the perimeters are equal, we set up the equation: \[ 6s = 4(s + 19) \]

Step 2: Solve the Equation

Simplify and solve the equation: \[ 6s = 4s + 76 \] Subtract \( 4s \) from both sides: \[ 2s = 76 \] Divide both sides by 2: \[ s = 38 \]

Step 3: Calculate the Side Length of the Square

The side length of the square is \( s + 19 \): \[ s + 19 = 38 + 19 = 57 \]

Final Answer

Length of one side of the square: \(\boxed{57}\) feet

Length of one side of the hexagon: \(\boxed{38}\) feet

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Exercise 23-9 (Algo) Segment elimination LO P4 [The following information applies to the questions displayed below.] Suresh Company reports the following segment (department) income results for the year. Department M Department N Department O Department P Department T Total --------------------- Sales 88,000 46,000 84,000 72,000 45,000 335,000 Avoidable 19,300 47,800 18,800 23,500 54,900 164,300 Unavoidable 59,400 24,000 6,100 59,100 23,100 171,700 Total expenses 78,700 71,800 24,900 82,600 78,000 336,000 Income (loss) 9,300 (25,800) 59,100 (10,600) (33,000) (1,000) Exercise 23-9 (Algo) Part 2 b. Compute the total increase in income if the departments with sales less than avoidable costs, as identified in part a, are eliminated.
failedAnswered
Question 9 (1 point) 9 At what age does difficulty in focusing close up typically begin? 30 s 40 s 50s 60 s
failedAnswered
In three independent flips of a coin where there is a 65% chance of flipping a head, let A denote first flip is a head, B denote second flip is a head, C denote first two flips are heads, and D denote three heads on the first three flips. Find the probabilities of A, B, C, and D, and determine which, if any, pairs of these events are independent. P(A)= (Round to two decimal places as needed.)
failedAnswered
Set up an equation that can be used to solve the problem. Solve the equation and determine the desired value. When sales representatives for a pharmaceutical company drive to out-of-town meetings that require an overnight stay, they receive 160 for lodging plus 0.65 per mile driven. How many miles did Joe drive if his company reimbursed him 322.50 for an overnight trip? The equation is .
failedAnswered
A sample of a substance with the empirical formula XBr2 weighs 0.4895 g. When it is dissolved in water and all its bromine is converted to insoluble AgBr by addition of an excess of silver nitrate, - XBr2 + 2 AgNO3 -> 2 AgBr + X(NO3)2 (a) Calculate the formula mass of XBr2. Formula mass XBr2= g mol^-1 (b) Calculate the atomic mass of X. Atomic mass X= g mol^-1