Question
Construct a rectangle $ABCD$ whose adjacent sides are $11\ cm$ and $8.5\ cm.$
✓
Answer
Steps of construction:
Step 1: Draw $AB = 11\ cm.$
Step 2: Make
$\angle\text{A}=90^\circ$
$\angle\text{B}=90^\circ$
Step 3: Draw an arc of $8.5\ cm$ from point $A$ and name that point as $D.$
Step 4: Draw an arc of $8.5\ cm$ from point $B$ and name that point as $C.$
Step 5: Join $C$ and $D.$
Thus, $ABCD$ is the required rectangle.
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Salma and Abid factorise the algebraic expression $p^4+9 p^2+18$
Salma
$
\begin{aligned}
p^4+9 p^2+18 & =p^4+6 \rho^2+3 p^2+18 \\
& =p^2\left(p^2+6\right)+3\left(p^2+6\right) \\
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\end{aligned}
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Abid
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\begin{aligned}
p^4+9 p^2+18 & =p^4+6 p+3 p+18 \\
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Who is correct? Give a reason to justify your answer.
→Salma
$
\begin{aligned}
p^4+9 p^2+18 & =p^4+6 \rho^2+3 p^2+18 \\
& =p^2\left(p^2+6\right)+3\left(p^2+6\right) \\
& =\left(p^2+3\right)\left(p^2+6\right)
\end{aligned}
$
Abid
$
\begin{aligned}
p^4+9 p^2+18 & =p^4+6 p+3 p+18 \\
& =p\left(p^3+6\right)+3(p+6) \\
& =\left(p^3+6\right)(p+6)(p+3)
\end{aligned}
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Who is correct? Give a reason to justify your answer.
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