Rectangle A has one side that is 6 cm long and the other is \((x+2)\) cm long. Rectangle Y has sides of length \((2x+1)\) cm and 3 cm. If the perimeters are the same, calculate the value of \(x\) and hence, the lengths of the sides of the rectangles.
Answer (2)
Hello,
Rectangle A: 6cm (x+2)cm Rectangle B: 3cm (2x+1)cm
The formula for the perimeter of a rectangle is: P=2(base+height)
Then:
P A = 2 ( b + h ) P A = 2 ∗ [ 6 + ( x + 2 )] P A = 2 ∗ ( x + 8 ) P A = 2 x + 16 P B = 2 ( b + h ) P B = 2 ∗ [ 3 + ( 2 x + 1 )] P B = 2 ∗ ( 2 x + 4 ) P B = 4 x + 8
But we know that the perimeters are the same, so:
P A = P B 2 x + 16 = 4 x + 8 8 = 2 x x = 4 R e pl a c in g : L e n g h t o f A = ( x + 2 ) c m L e n g h t o f A = ( 4 + 2 ) c m L e n g h t o f A = 6 c m L e n g h t o f B = ( 2 x + 1 ) c m L e n g h t o f B = ( 2 ∗ 4 + 1 ) c m L e n g h t o f B = 9 c m
With the answer of A, we realize that this figure is actually a square.
The value of x is 4, leading to side lengths of 6 cm for Rectangle A and 9 cm and 3 cm for Rectangle Y. Rectangle A is a square with all sides equal. Rectangle Y has one side shorter than the other.
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