Answer:
Explanation:
Let's call the side lengths of the first quadrilateral a, b, c, and d, and the side lengths of the second quadrilateral A, B, C, and D. We are given that the perimeter of the second quadrilateral is 20 cm, and that the quadrilaterals are similar. This means that the ratio of the side lengths of the two quadrilaterals is the same for all four sides. Let's call this ratio r. Then we have:
A + B + C + D = 20 cm
and
A/a = B/b = C/c = D/d = r
We can find the value of r by taking the ratio of any two sides of the quadrilaterals. For example, we can take the ratio of A to a:
A/a = r
Substituting the expressions for A and a in terms of r, we get:
(ra)/a = r
Solving for r, we get:
r = a/a = 1
This means that the ratio of the side lengths of the two quadrilaterals is 1. Therefore, the side lengths of the second quadrilateral are equal to the side lengths of the first quadrilateral. Substituting the given values for the side lengths of the first quadrilateral, we get:
A = 6 cm
B = 5 cm
C = 8 cm
D = 11 cm
Therefore, the side lengths of the second quadrilateral are A = 6 cm, B = 5 cm, C = 8 cm, and D = 11 cm.