a square and a rectangle have the same perimeteruare

Question

a square and a rectangle have the same perimeter. the length of the rectangle is 4cm less than twice the side of the square, and the width of the rectangle is 6cm less than the side of the square. find the perimeter of each figure
Let S be the side of the square and l,b be the dimensions of rectangle.
perimeters are same.

Answer 1

Cierra,

 

This problem is written specifically so we have to use what they give us. S is the side of the square so the length l is 2S-4. The width b is S-6. Now we know the perimeter of the square is 4S and the rectange is 2(2S-4)+2(S-6). Set these equal to each other:

4S-8+2S-12=4S

-20+2S=0

S=10

 

So the dimensions of the rectangle is 16x4. Checking our work, the total perimeter of the square is 40 so the perimeter of the rectangle should be as well: 2*16+2*4=32+8=40. Check. Hope that helps!