Respuesta :
Answer:
One possible dimensions is: If Rectangle B is 1x2 then Rectangle A is 0.315x12.685
Step-by-step explanation:
length of Rectangle A: a
width of Rectangle A: b
length of Rectangle B: c
width of Rectangle B: d
area of Rectangle A: a*b
area of Rectangle B: c*d
The area of Rectangle A is twice the area of Rectangle B:
2*c*d = a*b (eq. 1)
perimeter of Rectangle A: 2a + 2b
perimeter of Rectangle B: 2c + 2d
The perimeter of Rectangle A is 20 units greater than the perimeter of Rectangle B:
20 + 2c + 2d = 2a + 2b (eq. 2)
We have 4 variables (a, b, c and d) but only 2 equations, so we need to fix 2 variables and calculated the other ones. In this way, one of the infinite solutions is obtained. Selecting: c = 1 and d = 2, we get:
4 = a*b
26 = 2a + 2b
26b = 2a*b + 2b²
0 = 2b² -26b + 8
[tex]b = \frac{26 \pm \sqrt{(-26)^2 - 4(2)(8)}}{2(2)} [/tex]
[tex]b = \frac{26 \pm 24.739}{4} [/tex]
[tex]b_1 = \frac{26 + 24.739}{4} [/tex]
[tex]b_1 = 12.685[/tex]
[tex]b_2 = \frac{26 - 24.739}{4} [/tex]
[tex]b_2 = 0.315[/tex]
with b = 12.685, a = 4/12.685 = 0.315
with b = 0.315, a = 4/0.315 = 12.685
