Question

The perimeter of the rectangle is 22 meters, and the perimeter of the triangle is 12 meters. Find the dimensions of the rectangle.

Answer 1

Answer:

Length:8 m

Width:3 m

Step-by-step explanation:

The complete question is

If the perimeter of a rectangle is 22 meters, and the perimeter of a right triangle is 12 meters (the sides of the triangle are half the length of the rectangle, the width of the rectangle, and the hypotenuse is 5 meters). How do you solve for L and W, the dimensions of the rectangle.

step 1

Perimeter of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

we have

$P=22\ m$

so

$22=2(L+W)$

Simplify

$11=L+W$ -----> equation A

step 2

Perimeter of triangle

The perimeter of triangle is equal to

$P=\frac{L}{2}+W+5$

$P=12\ m$

so

$12=\frac{L}{2}+W+5$

Multiply by 2 both sides

$24=L+2W+10$

$L+2W=14$ ----> equation B

Solve the system of equations by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (8,3)

see the attached figure

therefore

The dimensions of the rectangle are

Length:8 m

Width:3 m