13. A rectangle has a width that is twice as long as its length and an area of 722 square inches. Find the length of the diagonal, rounded to the nearest tenth.

The diagonal of the rectangle is approximately 42.5 inches.

Step-by-step explanation:

The area of a rectangle is given by the following formula:

area = width*length

In this case the width = 2*length, therefore we have:

area = 2*length²

722 = 2*length²

2*length² = 722

length² = 361

length = sqrt (361) = 19 inches

width = 2*length = 2*19 = 38 inches

The diagonal forms a right triangle with the sides of the rectangle, where it is the hypotenuse. Therefore we can use Pytagora's theorem:

diagonal = sqrt (length² + width²)

diagonal = sqrt (19² + 38²) = 42.485 inches

The diagonal of the rectangle is approximately 42.5 inches.

42.5 inches

Step-by-step explanation:

l = length

w = 2l

A = 722

A = l*w

722 = l * 2l

722 = 2l^2

Divide each side by 2

361 = l^2

Take the square root of each side

sqrt (361) = l

w = 2 * sqrt (361)

We want to find the diagonal so we can use the pythagorean theorem

a^2 + b^2 = c^2 where c is the length of the diagonal

l^2 + w^2 = c^2

(sqrt (361)) ^2 + (2 sqrt (361)) ^2 = c^2

361+1444 = c^2

1805 = c^2

Take the square root of each side

sqrt (1805) = sqrt (c^2)

42.48529 = c

To the nearest tenth

42.5 = c