## momomalinka 3 years ago what is the easiest and fastest way to solve this? Nine playing cards from the same deck are placed as shown in the figure below to form a large rectangle of area 180 sq. in. How many inches are there in the perimeter of this large rectangle?

|dw:1343519419666:dw| they are all the same size I just can't draw

2. Romero

This can be anything....

3. Romero

do we know the measurements of the cards or a better picture?

|dw:1343519858074:dw| does that make you happy?

5. Romero

w*l=180 2*w+2*l=? This is a system of equations with an infinite number of solutions because we don't have enough information

Iit HAS an answer the answer is 58 but I don't know how to get there

7. UnkleRhaukus

$P=6\ell+7w$

8. silverninja

The short sides are 4s and the longer ones are 5s

9. UnkleRhaukus

$A=5w\times(w+l)$

10. eohjelle

From the illustration we can see that 5 breadths are equal to 4 lengths, which is equal to the length of the whole rectangle. 5b = 4l = L We also know the area of the large rectangle. From this we can create a system of equations, which we can use to solve. Notice also that the height of the rectangle is equal to a breadth and a length. h = b + l Now for the system of equations, which expresses the area (given by A = h*L): (b+l)*5b=180 (1) (b+l)*4l=180 (2) If we solve this system of equations we will get a value for the breadth and width, which we can use to find the perimeter.

okay so 5b^2+5Bl=180 and 4lb+4l^2=180 then use the process of elimination?

i did 20b^2+20bl=720 multiplied by 4 + -20l^2-20bl=-900 multiplied by -5 20bl cancels out so 20b^2-20l^2=-180 now what????

13. eohjelle

Now you have to find an expression for either b^2 or l^2 and substitute into one of the original equations :)