Question

i can solve problems involving shapes where the scale factor is known or can be found. 2. in each pair of similar shapes, work out the missing side length and explain how you calculated them: triangle missing side length: how i know: square missing side length: how i know: rectangle missing side length: how i know:

Explanation:

Step1: Find scale - factor for triangles

The corresponding sides of the two similar triangles are 4m and 8m. The scale - factor $k=\frac{8}{4}=2$.

Step2: Calculate missing side of triangle

The side corresponding to the 5m side in the smaller triangle in the larger triangle is $5\times2 = 10$m.

Step3: Find scale - factor for squares

The corresponding sides of the two similar squares are 3m and 9m. The scale - factor $k=\frac{9}{3}=3$.

Step4: Calculate missing side of square

Since all sides of a square are equal, the missing side is 9m.

Step5: Find scale - factor for rectangles

The corresponding sides of the two similar rectangles are 1m and 4m. The scale - factor $k = \frac{4}{1}=4$.

Step6: Calculate missing side of rectangle

The side corresponding to the 4m side in the smaller rectangle in the larger rectangle is $4\times4=16$m.

Answer:

Triangle missing side length: 10m
How I know: Found scale - factor of 2 from corresponding sides 4m and 8m, then multiplied 5m by 2.
Square missing side length: 9m
How I know: Found scale - factor of 3 from corresponding sides 3m and 9m, and all sides of a square are equal.
Rectangle missing side length: 16m
How I know: Found scale - factor of 4 from corresponding sides 1m and 4m, then multiplied 4m by 4.