Need help please!!! thanks!!!

Question

If the perimeter of a rectangle is 44 cm and the area is 117 square cm, then what are the dimensions of the rectangle?

Answer 1

117=3*3*13=9*13

9+13=22 and 2*22=44

the rectangle is 9 cm by 13 cm

Answer 2

Length= L

Width= W

Perimeter= 44cm

Area= 117cm²

 

Perimeter = 2L + 2W

Area = L x W

 

Therefore;

 

44= 2L + 2W  which can be reduced to 22= L + W

117= LW

L + W = 22, solve for L by subtracting w from both sides: L = 22-W

 substitute L = 22-W into the second equation: 117 = (22-W)W

                                                                     117= 22W-W²

Rearrange the equation: W²-22W+117=0

solve for W                    (W-13)(W-9)=0 so, W=13 and or 9

 

Substitute into 117=LW

W=13      117=13L divide both sides by 13 and L=9

W= 9       117=9L divide both sides by 9 and L= 13

 

Finally the dimensions of the rectangle are L= 13 and W= 9