The ratio of the length of a rectangular field to its width is 10:7 if the width of the field is 70 meters find the perimeter of the field.
length = L
width = w
Ratio = L:w = 10:7 = L:70
10:7 = L:70
10/7 = L/70
cross multiply
700 = 7L
L = 100
L = 100, w = 70
P = 2w + 2L
P = ?
To find the perimeter of the rectangular field, we need to know the length of the field.
Given that the ratio of the length to the width is 10:7, we can set up a proportion to solve for the length.
Let's represent the length of the field as L. The given width is 70 meters, so the proportion can be set up as:
L / 70 = 10 / 7
To solve this proportion, we can cross-multiply:
7L = 70 * 10
7L = 700
Finally, divide both sides by 7 to isolate L:
L = 700 / 7
L = 100
Therefore, the length of the field is 100 meters.
Now, we can find the perimeter by using the formula P = 2(L + W), where P is the perimeter, L is the length, and W is the width.
Substituting the values we found:
P = 2(100 + 70)
P = 2(170)
P = 340
Therefore, the perimeter of the field is 340 meters.
let the length be 10x
let the width be 7x , ( notice the ratio 10x : 7x = 10:7 )
given : 7x = 70
x = 10
Perimeter = 2(10x+7x) = 34x = 340
check:
length =100
width =70
perilmeter = 100+100+70+70 = 340