Rectangle ABCD is similar to rectangle WXYZ. If the area of rectangle ABCD is 70 square inches, AD is 10 inches, and XY is 5 inches, what is the area of rectangle WXYZ? Round to the nearest integer.

The area of rectangle WXYZ is 18 square inches

Step-by-step explanation: Since both rectangles are similar, then lines AD and BC has a common ratio with lines WZ and XY. If line line AD is 10 inches, and line XY is 5 inches, then the ratio of similarity is given as

Ratio = 10/5

Ratio = 2/1 (or 2:1)

However rectangle ABCD has its area as 70 square inches, which means the other side is given as

Area = L x W

70 = 10 x W

70/10 = W

7 = W

Therefore the width of the other rectangle is determined as,

10/5 = 7/W

10W = 5 x 7

10W = 35

Divide both sides of the equation by 10

W = 3.5

Having calculated the width of the other rectangle as 3.5, the area is now determined as

Area = L x W

Area = 5 x 3

Area = 17.5

Rounded off to the nearest integer, the area equals 18 square inches

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15