Question

Complete the following tables 1 and 3 only.

Answer 1

(a) D = 5/8 in

(b) A = 31.2 cm

(c) B = 8 ft

(d) C = 3 m

Step-by-step explanation:

If two triangles are similar, their corresponding sides are proportional, so we can always use the following equation:

`(A)/(B)=(C)/(D)`

Therefore, for row (a), we can write the following equation:

`(5(1)/(2))/(1(1)/(4))=(2(3)/(4))/(D)`

So, changing the mixed number by decimals and solving for D, we get:

`\begin{gathered} (5.5)/(1.25)=(2.75)/(D) \\ 5.5D=2.75(1.25) \\ 5.5D=3.4375 \\ (5.5D)/(5.5)=(3.4375)/(5.5) \\ D=0.625 \end{gathered}`

Then, for row (a), D = 0.625 = 5/8

In the same way, we can write and solve the following equation for row (b)

`\begin{gathered} (A)/(23.4)=(20.8)/(15.6) \\ (A)/(23.4)*23.4=(20.8)/(15.6)*23.4 \\ A=31.2 \end{gathered}`

For row (c), we get:

`\begin{gathered} (12)/(B)=(9)/(6) \\ 12(6)=9(B) \\ 72=9B \\ (72)/(9)=(9B)/(9) \\ 8=B \end{gathered}`

For row (d), we get:

`\begin{gathered} (4.5)/(3.6)=(C)/(2.4) \\ (4.5)/(3.6)*2.4=(C)/(2.4)*2.4 \\ 3=C \end{gathered}`

Therefore, the answers are:

(a) D = 5/8 in

(b) A = 31.2 cm

(c) B = 8 ft

(d) C = 3 m