Question

directions: complete the following questions by showing all work and annotations. keep work organized and box any final answer. all work must be shown in order to receive full credit. #1.) in the figure below, (overline{fg}) is 60 cm. find the length of (overline{fh}). reminder! part + part = whole **#2.) determine the length of (overline{dg}).

Explanation:

Step1: Set up equation for problem 1

Since $FH + HG=FG$, we have $(4x - 3)+(2x + 21)=60$.
Combining like - terms: $4x+2x-3 + 21=60$, which simplifies to $6x+18 = 60$.
Subtract 18 from both sides: $6x=60 - 18$, so $6x=42$.
Divide both sides by 6: $x = 7$.

Step2: Find length of $FH$

Substitute $x = 7$ into the expression for $FH$ which is $4x-3$.
$FH=4\times7-3=28 - 3=25$ cm.

Step3: Set up equation for problem 2

From the figure, $DE+EF+FG=DG$. Also, we can set up an equation based on the given expressions.
We know that $DE + EF=14x + 3$ and $EF = 12$, $FG=21$, and $DE+EF=11x$.
So, $11x+21=14x + 3$.
Subtract $11x$ from both sides: $21=14x-11x + 3$, which simplifies to $21 = 3x+3$.
Subtract 3 from both sides: $3x=21 - 3=18$.
Divide both sides by 3: $x = 6$.

Step4: Find length of $DG$

$DG=14x+3$. Substitute $x = 6$ into the expression.
$DG=14\times6+3=84 + 3=87$.

Answer:

1. The length of $FH$ is 25 cm.
2. The length of $DG$ is 87.