Question 949668
The perimeter of a rectangle is 14cm. If the diagonal is 5cm, find the dimensions of the rectangle.
L=Length; W=width; D=Diagonal; P=perimeter=2(L+W)
{{{D=sqrt(L^2+W^2)}}}
{{{5cm=sqrt(L^2+W^2)}}} square each side
{{{25 sq cm=(L^2+W^2)}}}
P=2(L+W)
14 cm=2(L+W) Divide each side by 2.
7 cm=L+W Subtract W from each side
7 cm-W=L
{{{25 sq cm=(L^2+W^2)}}} Substitute for L
{{{25 sq cm=(7cm-W)^2+W^2)}}}
{{{25 sq cm=W^2-14W+49+W^2}}} Subtract 25 cm from each side.
{{{0=2W^2-14W+24cm}}}*[invoke quadratic "W", 2, -14, 24 ]
ANSWER The answers are 3 cm and 4 cm, so when width=3 cm, length=4 cm and when width=4 cm, length=3 cm.
CHECK
P=2(L+W)
14 cm=2(4 cm+3 cm)
14 cm=2(7 cm)
14 cm=14 cm
Diagonal=5
{{{D=sqrt(L^2+W^2)}}}
{{{5 cm=sqrt(4^2+3^2)}}}
{{{5 cm=sqrt(16+9)}}}
{{{5 cm=sqrt(25 cm^2)}}}
{{{5 cm=5 cm}}}