math
posted by alison .
the perimeter of a rectangle is 22 meters, and the perimeter of the triangle is 12 meters. find the dimensions of the rectangle?

Let l be the length, and w be the width, of the rectangle.
The perimeter of the rectangle is 2(l+w).
The perimeter of the triangle is l+w+sqrt(l^2+w^2). sqrt(l^2+w^2) is the hypotenuse of the triangle.
There are two equations and two variables. Find l and w. 
the hypotneuse is 5 meters so how could i figure the dimensions of the rectangle out?

The perimeter of the rectangle is 22m. So 2(l+w) = 22.
l+w = 11
l = 11w
Also, l^2+w^2 = 5^2 by Pythagorean Theorem.
Substitute in l = 11w: (11w)^2+w^2=5^2 
i have the deminsions of the rectangle but i need to know how to get it , the deminsions are 8m by 3m

Are you referring to the triangle formed by the diagonal of the rectangle and two of its sides? If the dimensions are 8m by 3m, the hypotenuse of said triangle cannot be 5m.

im referring to the deminsions of a rectangle with a triangle with a hypotneuse of 5m in the top right corner

Is the base of the triangle the width of the rectangle, and the height of the triangle half the length of the rectangle?

yes it certainly is

Ok. Then the perimeter of the triangle is w + l/2 + 5.
So w+l/2+5 = 12m, and 2(l+w)=22m. 
thank you so very much you are awesome i wish you were my math teacher!

you are going to end up hating me i am really bad at dimensions so please bear with me.
a dorm room your sister is considering seems small.the room is rectangular and has a perimeter of 42 feet. the room is 4 feet longer than its width. what are the dimensions of the room? 
Alison  please post your last question as a separate post.

nevermind i got it thanks anyway!
Respond to this Question
Similar Questions

basic geometric
10. a rectangle has width the same as a side of a square whose perimeter is 20m. the length of the rectangle is 9m. find the perimeter of this rectangle. 34. The width of a rectangular picture is onehalf the length. The perimeter … 
basic geometry
A rectangle has width the same asa a side of a square whose perimeter is 20m.the length of the rectangle is 9m. Find the perimeter of this rectangle. 34. The with of a rectangular picture is onhalf the length . The perimeter of the … 
pre calculus
The perimeter of a rectangle is 480 meters and its length is 1.5 times its width. find the dimensions of the rectangle. 
Geometry
Can you check these multiple choice questions thanks. 1. What is the length of a rectangle that has an area of 20 square meters and a perimeter of 18 meters. A. 10 meters B. 2 meters C. 5 meters D. 9 meters Answer: B 2. Find the minimum … 
math
the length of a rectangle is 5 ft more than twice the width. a)if x represents the width of the rctangle, represent the perimeter of the rectangle in terms of x. b) if the perimeter if the rectangle is 2 ft more than eight times the … 
Perimeter
A rectangle has a perimeter of 12m. If each side is a whole number of meters, what are the possible dimensions for the length and width? 
math concepts and applications
A rectangle has a length of 6 meters and a perimeter of 20 meters. What is the width of the rectangle? 
Solving Geometry Formulas
The perimeter of a rectangle is 56 meters. If the width of the rectangle is 7 meters, find the length. 
Math
The length of a rectangle is 8 meters less than 5 times its width. if the perimeter of the rectangle is at most 104 meters, find the greatest possible width of the rectangle. 
Mathematics
The width of a rectangle is 20m less than twice its length. If the perimeter of the rectangle is more than 56m, find the minimum dimensions of the rectangle if each dmension in meters is an integer.