write number sentences and solve these problems.
(1)
the perimeter of a triangle is $27\frac{2}{3}$ ft. two of the sides measure $10\frac{1}{6}$ ft. each. what is the length of the third side? circle your final answer.
(2)
what is the perimeter of a rectangle that is $3\frac{3}{10}$ cm long and $2\frac{7}{10}$ cm wide?
(3)
what is the area of a rectangle that is $2\frac{1}{4}$ yd. long and $1\frac{1}{2}$ yd. wide?
(4)
one side of a square is $6\frac{1}{4}$ units. use multiplication to find the perimeter of the square.
multiply.
(5) $1\frac{1}{9}\times4\frac{1}{5}=$
(8) $14\times\frac{3}{4}=$
(6) $8\times5\frac{1}{4}=$
(9) $4\frac{2}{3}\times1\frac{2}{7}=$
(7) $3\frac{3}{5}\times\frac{10}{21}=$
(10) $\frac{7}{8}\times\frac{20}{21}=$

Question

Accepted Answer

# Answer:
(1) $ 7\frac{1}{3}$ ft.
(2) $ 12$ cm.
(3) $ 3\frac{3}{8}$ yd².
(4) $ 25$ units.
(5) $ 4\frac{8}{15}$.
(6) $ 42$.
(7) $ 1\frac{3}{7}$.
(8) $ 10\frac{1}{2}$.
(9) $ 7\frac{1}{3}$.
(10) $ 1\frac{1}{6}$.

# Explanation:
## Step1: Solve problem (1)
The perimeter of a triangle $P=a + b + c$. Given $P = 27\frac{2}{3}=\frac{83}{3}$, $a=b = 10\frac{1}{6}=\frac{61}{6}$.
$$
\begin{align*}
c&=\frac{83}{3}-2\times\frac{61}{6}\
&=\frac{83}{3}-\frac{61}{3}\
&=\frac{83 - 61}{3}\
&=\frac{22}{3}=7\frac{1}{3}
\end{align*}
$$
## Step2: Solve problem (2)
The perimeter of a rectangle $P = 2(l + w)$. Given $l=3\frac{3}{10}=\frac{33}{10}$, $w = 2\frac{7}{10}=\frac{27}{10}$.
$$
\begin{align*}
P&=2(\frac{33}{10}+\frac{27}{10})\
&=2\times\frac{33 + 27}{10}\
&=2\times\frac{60}{10}\
&=12
\end{align*}
$$
## Step3: Solve problem (3)
The area of a rectangle $A=l\times w$. Given $l = 2\frac{1}{4}=\frac{9}{4}$, $w=1\frac{1}{2}=\frac{3}{2}$.
$$
\begin{align*}
A&=\frac{9}{4}\times\frac{3}{2}\
&=\frac{27}{8}=3\frac{3}{8}
\end{align*}
$$
## Step4: Solve problem (4)
The perimeter of a square $P = 4s$. Given $s=6\frac{1}{4}=\frac{25}{4}$.
$$
\begin{align*}
P&=4\times\frac{25}{4}\
&=25
\end{align*}
$$
## Step5: Solve problem (5)
$1\frac{1}{9}=\frac{10}{9}$, $4\frac{1}{5}=\frac{21}{5}$
$$
\begin{align*}
\frac{10}{9}\times\frac{21}{5}&=\frac{10\times21}{9\times5}\
&=\frac{210}{45}\
&=\frac{14}{3}=4\frac{8}{15}
\end{align*}
$$
## Step6: Solve problem (6)
$5\frac{1}{4}=\frac{21}{4}$
$$
\begin{align*}
8\times\frac{21}{4}&=\frac{8\times21}{4}\
&=42
\end{align*}
$$
## Step7: Solve problem (7)
$3\frac{3}{5}=\frac{18}{5}$
$$
\begin{align*}
\frac{18}{5}\times\frac{10}{21}&=\frac{18\times10}{5\times21}\
&=\frac{180}{105}\
&=\frac{12}{7}=1\frac{3}{7}
\end{align*}
$$
## Step8: Solve problem (8)
$$
\begin{align*}
14\times\frac{3}{4}&=\frac{14\times3}{4}\
&=\frac{42}{4}=10\frac{1}{2}
\end{align*}
$$
## Step9: Solve problem (9)
$4\frac{2}{3}=\frac{14}{3}$, $1\frac{2}{7}=\frac{9}{7}$
$$
\begin{align*}
\frac{14}{3}\times\frac{9}{7}&=\frac{14\times9}{3\times7}\
&=6=\frac{22}{3}=7\frac{1}{3}
\end{align*}
$$
## Step10: Solve problem (10)
$$
\begin{align*}
\frac{7}{8}\times\frac{20}{21}&=\frac{7\times20}{8\times21}\
&=\frac{140}{168}\
&=\frac{5}{6}=1\frac{1}{6}
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Solve problem (1)

Step2: Solve problem (2)

Step3: Solve problem (3)

Step4: Solve problem (4)

Step5: Solve problem (5)

Step6: Solve problem (6)

Step7: Solve problem (7)

Step8: Solve problem (8)

Step9: Solve problem (9)

Step10: Solve problem (10)

Answer: