Question

the length and width of rectangles are given. use the formula a = l × w for exercises 6 to 11. 6. l = 10 in.; w = 5 in.; find a. 7. l = 6 m; w = 1 m; find a. 8. l = 125 mi; w = 4 mi; find a. 9. l = 35 ft; w = 6 ft; find a. 10. l = 25 m; w = 4 m; find a. 11. l = 10 in.; w = 10 in.; find a. a math teacher found that students’ grades g on an exam are related to the number of hours studied h by the formula g = 11h + 63. use this formula for exercises 12 to 14. 12. h = 1 hour, find g. 13. h = 3 hours, find g. 14. h = 2 hours, find g. use the formula f = 1.8c + 32 for exercises 15 to 17. 15. c = 30°. find f. 16. c = 15°. find f. 17. c = 4°. find f. feliz has 5 weeks to save money for vacation. the formula s = 5d gives the total amount he will save, s, if he saves d dollars a week. use the formula for exercises 18 to 20. 18. d = 8, find s. 19. d = 10, find s. 20. d = 4, find s. 21. reasoning the length of a rectangle is 12 meters. which would give a greater area, if w = 4 or w = 6? explain.

Explanation:

Step1: Recall area formula

The area formula for a rectangle is $A = l\times w$.

Step2: Solve exercise 6

Substitute $l = 10$ in. and $w = 5$ in. into the formula: $A=10\times5 = 50$ in.$^{2}$.

Step3: Solve exercise 7

Substitute $l = 6$ m and $w = 1$ m into the formula: $A = 6\times1=6$ m$^{2}$.

Step4: Solve exercise 8

Substitute $l = 125$ mi and $w = 4$ mi into the formula: $A=125\times4 = 500$ mi$^{2}$.

Step5: Solve exercise 9

Substitute $l = 35$ ft and $w = 6$ ft into the formula: $A=35\times6=210$ ft$^{2}$.

Step6: Solve exercise 10

Substitute $l = 25$ m and $w = 4$ m into the formula: $A = 25\times4=100$ m$^{2}$.

Step7: Solve exercise 11

Substitute $l = 10$ in. and $w = 10$ in. into the formula: $A=10\times10 = 100$ in.$^{2}$.

Step8: Solve exercise 12

For the formula $g = 11h+63$, substitute $h = 1$: $g=11\times1 + 63=11 + 63=74$.

Step9: Solve exercise 13

Substitute $h = 3$ into $g = 11h+63$: $g=11\times3+63=33 + 63 = 96$.

Step10: Solve exercise 14

Substitute $h = 2$ into $g = 11h+63$: $g=11\times2+63=22 + 63=85$.

Step11: Solve exercise 15

For the formula $F = 1.8C+32$, substitute $C = 30$: $F=1.8\times30+32=54 + 32=86$.

Step12: Solve exercise 16

Substitute $C = 15$ into $F = 1.8C+32$: $F=1.8\times15+32=27+32 = 59$.

Step13: Solve exercise 17

Substitute $C = 4$ into $F = 1.8C+32$: $F=1.8\times4+32=7.2+32 = 39.2$.

Step14: Solve exercise 18

For the formula $s = 5d$, substitute $d = 8$: $s=5\times8=40$.

Step15: Solve exercise 19

Substitute $d = 10$ into $s = 5d$: $s=5\times10 = 50$.

Step16: Solve exercise 20

Substitute $d = 4$ into $s = 5d$: $s=5\times4=20$.

Step17: Solve exercise 21

For $l = 12$ m, when $w = 4$ m, $A_1=12\times4 = 48$ m$^{2}$. When $w = 6$ m, $A_2=12\times6=72$ m$^{2}$. Since $72>48$, $w = 6$ gives a greater area because the area of a rectangle $A=l\times w$ and when the length is fixed, a larger - width results in a larger area.

Answer:

1. 50 in.$^{2}$
2. 6 m$^{2}$
3. 500 mi$^{2}$
4. 210 ft$^{2}$
5. 100 m$^{2}$
6. 100 in.$^{2}$
7. 74
8. 96
9. 85
10. 86
11. 59
12. 39.2
13. 40
14. 50
15. 20
16. $w = 6$ gives a greater area. When $l = 12$ m and $w = 4$ m, $A = 48$ m$^{2}$; when $w = 6$ m, $A = 72$ m$^{2}$. Since the area formula is $A=l\times w$ and $l$ is fixed, a larger $w$ leads to a larger $A$.