SOLUTION: The perimeter of a rectangle is 14cm. If the diagonal is 5cm, find the dimensions of the rectangle.

Algebra.Com
Question 949668: The perimeter of a rectangle is 14cm. If the diagonal is 5cm, find the dimensions of the rectangle.
Answer by macston(5194)   (Show Source): You can put this solution on YOUR website!
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)

square each side

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
Substitute for L

Subtract 25 cm from each side.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=4 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 4, 3. Here's your graph:

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
RELATED QUESTIONS

find the dimensions of a rectangle if the area is 4cm and the perimeter is 14cm (answered by checkley77)
The perimeter of a rectangle is 18cm. The area is 14cm^2. Find the... (answered by oscargut)
The perimeter of a rectangle is 68cm. If the diagonal is 26cm, find the dimensions of the (answered by oberobic)
The perimeter of a rectangle is 50cm. if its length exceeds its breadth by 5cm,find the... (answered by mananth)
A rectangle is 5cm longer than it is wide. The diagonal of the rectangle is 18cm. What... (answered by ikleyn)
a rectangle has a perimeter of 18cm its length is 5cm more than the width. find the... (answered by checkley77)
the length of a rectangle is 5cm. greater than twice its width. if the perimeter is 52... (answered by sharon1948)
The width of a rectangle is 5cm less than the length. What are the dimensions of the... (answered by rfer)
a rectangle has a perimeter of 18cm. Its lenght is 5cm greater than its width. find the... (answered by mananth)