Mark made a scale drawing of a soccer field, using a scale of .5 cm=1m. the actual length of the field is 110 m. what is the length of the field on the drawing?
a.109.5 cm
b.110.5 cm
c.220 cm
d. 55 cm

The length of the field on the drawing is 55 cm that is option D.

Step-by-step explanation:

Given:

Mark made a scale drawing of a soccer field, using a scale of .5 cm=1 m.

The actual length of the field is 110 m.

Now, to find the length of the field on the drawing.

Let the length of the field on drawing be

As given,

Drawing of a soccer field, using a scale of 0.5 cm=1 m.

So, 0.5 cm is equivalent to 1 m.

Thus, is equivalent to 110 m.

Now, to get the length of the field on the drawing by using cross multiplication:

By cross multiplying we get:

Therefore, the length of the field on the drawing is 55 cm that is option D.

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240