Question

Rectangles ABCD and QRST are similar I 42 cm B 21 cm D (a) Determine the scale factor applied to rectangle ABCD to create rectangle QRST Show your work! 1 (b) Reproduce rectangle ABCD at a scale of Show your work and label measurements for each side of your rectangle.​

Answer 1

(a) Scale factor:
`k = (2)/(3)`

(b) See attachment

Explanation:

Given

See attachment for ABCD and QRST

Solving (a): The scale factor of ABCD to QRST

This is calculated as:

`k * ABCD = QRST`

Considering corresponding sides AB and QR

`AB = 42cm;\ QR = 28cm`

`k * AB = QR`

`k * 42 = 28`

Make k the subject

`k = (28)/(42)`

`k = (2)/(3)`

Solving (b): Reproduce ABCD at scale factor of
`(1)/(2)`

The new rectangle will have the following side lengths.

`AB' = (1)/(2) * AB`

`AB' = (1)/(2) * 42`

`AB' = 21`

`BC' = (1)/(2) * BC`

`BC' = (1)/(2) * 21`

`BC' = 10.5`