Question

Determine the coordinates of the corners of the rectangle to compute the perimeter of the rectangle using the distance formula (round to the nearest integer). A.) 30 units B.) 45 units C.) 50 units D.) 60 units

Answer 1

Answer:

Option B.) 45 units

Step-by-step explanation:

see the attached figure with letter to better understand the problem

step 1

Determine the coordinates of the corners of the rectangle

Let

A(4,5),B(1,8),C(14,21) and D(17,18)

step 2

we know that

The formula to calculate the perimeter of rectangle is equal to

$P=2(AB+BC)$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the length side AB

$A(4,5),B(1,8)$

substitute in the formula

$d=\sqrt{(8-5)^{2}+(1-4)^{2}}$

$d=\sqrt{(3)^{2}+(-3)^{2}}$

$d_A_B=\sqrt{18}\ units$

Find the length side BC

$B(1,8),C(14,21)$

substitute in the formula

$d=\sqrt{(21-8)^{2}+(14-1)^{2}}$

$d=\sqrt{(13)^{2}+(13)^{2}}$

$d_B_C=\sqrt{338}\ units$

Find the perimeter

$P=2(AB+BC)$

substitute the values

$P=2(\sqrt{18}+\sqrt{338})$

$P=45\ units$

Answer 2

Answer:

B) 45 units

Step-by-step explanation:

D = dx2 + dy2

W = (1-4)2 + (8-5)2

W = (-3)2 + (3)2 = 4.24264

L = (1-14)2 + (8-21)2

L = (-13)2 + (-13)2 = 18.38478

A = 2L+2W = 2(18.38478)+2(4.24264)= 45.3 units