Perimeter of the First
A square combine with a first rectangle which the long side of it equals to the side of a square to make a second rectangle which its perimeter equal to 26.The first rectangle combine with a square which side of it equals to the short side of the first rectangle to make a third rectangle which its perimeter is 22.Find the perimeter of the first rectangle.
The answer is 16.
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2 solutions
Perimeter of the second rectangle formula: 2 ( a + b + a ) = 2 ( 2 a + b ) = 4 a + 2 b = 2 6 ⟹ 2 a + b = 1 3
Perimeter of the third rectangle formula: 2 ( a + b + b ) = 2 ( a + 2 b ) = 4 b + 2 a = 2 2
2 a − 2 a + + 4 b b 3 b = = = 2 2 1 3 9
3 b = 9 ⟹ b = 3
2 a + 3 = 1 3 ⟹ 2 a = 1 0 ⟹ a = 5
2 ( 3 + 5 ) = 2 × 8 = 1 6
Relevant wiki: Similar Polygons - Area and Perimeter Relations
The second rectangle would have a perimeter of 2 × ( a + b + a ) = 2 a + 2 a + 2 b = 4 a + 2 b
and we know that 4 a + 2 b = 2 6 as stated in the question.
The third rectangle would have a perimeter of 2 × ( a + b + b ) = 2 a + 2 b + 2 b = 2 a + 4 b
Adding both equations up we have 6 a + 6 b = 2 6 + 2 2 ⟹ 4 8 dividing both sides by 3 and we have 2 a + 2 b = 1 6