, Fractions, Decimals, and Percents Use what you know about ratios, fractions, decimals, and percents to fill in the blanks with the appropriate equivalent forms. Make sure your fractions and ratios are in simplest form!

Words
Ratio
Fraction
Decimal
Percent

3:4

0.25

6 tenths

1/3

80%

19/20

1 and 5 tenths

7:8

words:6 tenths or 1 and 5 tenths

Ratio:3:4 or 7:8

Fraction=1/3 or 19/20

Decimal:0.25

Percent:80%

(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