Rectangle A has a length of 3y cm and a width of 2x cm. Rectangle B has a length of (y + 4)cm and a width of (x + 6)cm. Rectangle A has a perimeter of 94cm and Rectangle B has a perimeter of 56cm. Solve x and y and calculate the areas of each rectangle.
To calculate the perimeter of a shape, you have to add up the lengths of all of its sides. So:A: 3y + 2x + 3y + 2x = 94 ; B: (y + 4) + (x + 6) + (y + 4) +(x + 6) = 56Simplifying both equations give:4x + 6y = 94 ; 2x + 2y = 36. This can be further simplifyed by dividing both equations by 2. So:2x + 3y = 47 ; x + y = 18. Rearranging the second equation gives usx = 18 - y. Substitute this into the original equation:2(18 - y) +3y = 47 => 36 + y = 47. Therefore, y = 11. Therfore:x = 18 - y = 18 - 11 = 7.We can now calculate the areas:A: (3 * 11)(2*7) = 33 * 14 = 462 cm2B: (11 + 4)(7+6) = 15 * 13 = 195 cm2
