Time Remaining
1 answer:
Answer:
a. Length = 13 yards and Width = 21 yards.
b. Area of rectangle = 273 square yards.
Step-by-step explanation:
Let the length of the rectangular garden be L
Let the width of the rectangular garden be W
Given the following data;
Perimeter of garden = 68 yards
Translating the word problem into an algebraic equation, we have;
W = 2L - 5 ......equation 1
Note: The formula for calculating the perimeter of a rectangle is;
68 = 2L + 2W ........equation 2
Substituting eqn 1 into eqn 2;
68 = 2L + 2(2L - 5)
68 = 2L + 4L - 10
68 = 6L - 10
6L = 68 + 10
6L = 78
L = 78/6
L = 13 yards
To find the width;
W = 2L - 5
W = 2(13) - 5
W = 26 - 5
W = 21 yards.
b. To find the area of the garden;
Area of rectangle = length * width
Area of rectangle = 13 * 21
Area of rectangle = 273 square yards.
You might be interested in
first we try to semplify as much as possible the fractions.
First we decompose the numbers
789 = 3 * 263
548 = 2 * 2 * 137 = 2^2
they have nothing in common, so the first fraction remains so
89 = 89 (prime number)
887 = 887 (prime number)
they have nothing in common, so the second one remains so
688 = 2 * 2 * 2 * 2 * 43 = 2^4 * 43
8724 = 2 * 2 * 3 * 727 = 2^2 * 3 * 727
they have 2^2 (=4) in common, so the numerator and the denominator can be devided by 4
so:
now we calculate the common denominator
take the scomposition:
548 = 2^2 * 137
887 = 887
2181 = 3 * 727
take every number one time
so the common denominator is 2^2 * 137 * 887 * 727 * 3 = 1'060'131'756
now calculate every single numerator: first we divide each denominator by the common denominator, then we moltiply the result with each numerator
first fraction: 789/548
1060131756 / 548 = 1934547
1934547 * 789 = 1526357583
second fraction: 89/887
1060131756 / 887 = 1195188
1195188 * 89 = 106371732
third one: 172/2181
1060131756 / 2181 = 486076
486076 * 172 = 83605072
now we can delete the common denominator
1526357583x - 106371732 = 83605072
solve it
1526357583x = 83605072 + 106371732
1526357583x = 189976804
x = 1526357583 / 189976804
decompose
1526357583 = 887 * 3 * 3 * 727 * 263
189976804 = 137 * 2 * 2 * 211 * 53 * 31
nothing in common
x = 1526357583 / 189976804