Lara is putting lace trim around the border of a circular tablecloth. The tablecloth has a diameter of 1.2 meters. What is the length of the lace she needs? Round to the nearest tenth of a meter.

3.8m

Step-by-step explanation:

Since Lara is putting lace trim around the border of a circular tablecloth, by the time she finishes she has covered the circumference.

The circumference of a circle is calculated using:

where d is the diameter of the circle.

It was given that the diameter of the circular table cloth is 1.2 meters.

Therefore the length of the lace she needed is 3.8m

(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

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step-by-step explanation: