Question

In the diagram, RSTU - ABCD. Find the ratio of their perimeters. All I The ratio of their perimeters is

Answer 1

3:2

1) Since those quadrilaterals are similar, they have proportional sides. Therefore we can use the Thales Theorem about similarity and write:

`\begin{gathered} (BC)/(ST)=(CD)/(UT) \\ (8)/(12)=(14)/(UT) \\ 12\cdot14=8UT \\ UT=(12\cdot14)/(8) \\ UT=21 \end{gathered}`

2) Now we can find both perimeters since their opposite sides are congruent to each other.

2P (ABDC) = 8+8+14+14 = 16 +28 =44

2P( RSTU) = 2(12+21) = 2(33) = 66

3) Now we can write the ratio of Quadrilateral RSTU to ABCD

`\frac{\text{RSTU}}{\text{ABCD}}=(66)/(44)=(3)/(2)`

Hence the ratio between the perimeter of RSTU to ABCD is 3:2