Answer:
x = 2.5 mm
Step-by-step explanation:
A compound shape is made up of two or more basic shapes.
From inspection of the given compound shape, we can see that it is made up of two rectangles.
[tex]\boxed{\begin{minipage}{4 cm}\underline{Area of a rectangle}\\\\$A=w \cdot l$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\ \phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}[/tex]
Dimensions of the smaller rectangle:
Dimensions of the larger rectangle:
Therefore, the equation for the area of the compound shape is:
[tex]\begin{aligned}\implies \textsf{Area}&=x \cdot 4 + x \cdot (2x+3)\\&=4x+x(2x+3)\\&=4x+2x^2+3x\\&=2x^2+7x\end{aligned}[/tex]
Given the area of the compound shape is 30 mm², substitute this value into the found equation for area and solve for x:
[tex]\begin{aligned}\implies 2x^2+7x &=30\\2x^2+7x-30&=0\\2x^2+12x-5x-30&=0\\2x(x+6)-5(x+6)&=0\\(2x-5)(x+6)&=0\\\\2x-5&=0 \implies x=2.5\\x+6&=0 \implies x=-6\end{aligned}[/tex]
As length is positive, x = 2.5 mm only.
