Answer:
6468 mm²
Step-by-step explanation:
Given:
- 21 mm = length of the shortest of the small rectangle
- Let y = length of the longest of the small rectangle
Therefore, the area of the small rectangle is:
= width × length
= 21 × y
= 21y mm²
From inspection of the larger rectangle
- longest side length = 4 × 21 = 84 mm
- shortest side length = (2y + 21) mm
Therefore, the area of the larger rectangle is:
= width × length
= 84(2y + 21)
= 168y + 1764 mm²
We know that the area of the larger rectangle is 11 times the area of the smaller rectangle. Therefore,
⇒ 11 small rectangles = larger rectangle
⇒ 11(21y) = 168y + 1764
⇒ 231y = 168y + 1764
⇒ 63y = 1764
⇒ y = 28
Therefore, the missing side length of the smaller rectangle is 28 mm.
Finally, to find the area of the larger rectangle, substitute the found value of y into the found expression for its area:
⇒ area = 168y + 1764
⇒ area = 168(28) + 1764
⇒ area = 4704 + 1764
⇒ area = 6468 mm²
