Question

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Answer 1

Answer:

Question 10

$\begin{aligned}\textsf{Perimeter} & = 50\\\\\implies 7 + \dfrac{1}{2}x+(x-8) & = 50\\\\\dfrac{3}{2}x & =51\\\\x & = 34\end{aligned}$

Input found value of x to determine side lengths:

$\implies 7$

$\implies \dfrac{1}{2}(34)=17$

$\implies 34-8=26$

Therefore, the length of the smallest side is 7 units.

Question 11

$\begin{aligned}\textsf{Perimeter} & = 75\\\\\implies 21 + \dfrac{1}{2}x+(x+1) & = 75\\\\\dfrac{3}{2}x & =53\\\\x & = \dfrac{106}{3}\end{aligned}$

Input found value of x to determine side lengths:

$\implies 21$

$\implies \dfrac{1}{2}\left(\dfrac{106}{3}\right)=\dfrac{53}{3}=17\frac{2}{3}$

$\implies \dfrac{106}{3}+1=\dfrac{109}{3}=36\frac{1}{3}$

Therefore, the length of the smallest side is 17 ²/₃ units.

Answer 2

#10

• Perimeter=sum of sides

$\\ \rm\Rrightarrow 7+0.5x+x-8=50$

$\\ \rm\Rrightarrow 1.5x-1=50$

$\\ \rm\Rrightarrow 1.5x=51$

$\\ \rm\Rrightarrow x=34$

• Smallest side should be 7units

As 0.5x=17units and x-8=26units

#11

$\\ \rm\Rrightarrow x+1+21+0.5x=75$

$\\ \rm\Rrightarrow 1.5x+22=75$

$\\ \rm\Rrightarrow 1.5x=53$

$\\ \rm\Rrightarrow x=35.3$

• 0.5x=17.6
• x+1=36.3

Smallest side 21units