Respuesta :
Answer:
The possible dimensions are;
If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units
Step-by-step explanation:
Let;
Length of Rectangle A be a
Width of Rectangle A be b
Length of Rectangle B be c
Width of Rectangle B be d
Thus;
Area of Rectangle A = a × b
Area of Rectangle B = c × d
We are told that the area of Rectangle A is twice the area of Rectangle B:
Thus;
2cd = ab - - - - - eq. 1
perimeter of Rectangle A = 2a + 2b
perimeter of Rectangle B = 2c + 2d
We are told that the perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B. Thus, we now have;
20 + 2c + 2d = 2a + 2b - - - - eq. 2
We have 4 unknowns which are (a, b, c and d) but only 2 equations, so we need to reduce to 2 unknown variables and calculate the other ones. In this way, one of the infinite solutions is obtained.
Let's assume that c = 1 and d = 2, we obtain:
From eq 1, we have;
2 * 1 * 2 = a*b
ab = 4 or a = 4/b
From eq 2, we have;
20 + 2(1) + 2(2) = 2a + 2b
26 = 2a + 2b
Putting a = 4/b into this, we have;
26 = 2(4/b) + 2b
Multiply through by b to get;
26b = 8 + 2b²
So,we have;
2b² -26b + 8 = 0
Using quadratic formula for this,
b = 0.315 or 12.685
When, b = 12.685, a = 4/12.685 = 0.315
When, b = 0.315, a = 4/0.315 = 12.685
So, the possible dimensions are;
If Rectangle B has a dimension of 1 unit x 2 units, then Rectangle A has a dimension of 0.315 units x 12.685 units
