The perimeter of a rectangle is 56 meters. the ratio of its length to its width is 4: 3. what is the length in meters of a diagonal of the rectangle? show your ! will be the brainliest if answered

Work Shown:

L = length

W = width

"ratio of length to width is 4:3", so L/W = 4/3

Let's solve for L

L/W = 4/3

3L = 4W cross multiply

L = 4W/3 ... we'll use this later in the next section

P = perimeter of rectangle

P = 2*(L+W)

P = 2*(4W/3+W) ... replace L with 4W/3

P = 2*(4W/3+3W/3)

P = 2*(7W/3)

P = 14W/3

14W/3 = P

14W/3 = 56 ... plug in the given perimeter P = 56

14W = 56*3 ... multiply both sides by 3

14W = 168

W = 168/14 ... divide both sides by 14

W = 12

Use that value of W to find L

L = 4W/3

L = 4*12/3

L = 48/3

L = 16

As a check, L/W = 16/12 = 4/3

also the four sides add up to 12+16+12+16 = 56 which is the given perimeter

so we have the proper length and width values

Now we can find the diagonal. Note how a right triangle forms if you draw in one diagonal of the rectangle. The legs of the triangle are the length and width (L = 16, W = 12). The diagonal is the hypotenuse or longest side of the right triangle.

D = length of diagonal

D^2 = L^2+W^2 ... pythagorean theorem

D^2 = 16^2+12^2

D^2 = 256+144

D^2 = 400

D = sqrt(400) ... apply the square root to both sides

D = 20

answer are

step-by-step explanation: