NicoleSky25
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the area of the compound shape below is 30mm^2.
Calculate the value of x.
If your answer is a decimal, give it to 1 d.p

The Area Of The Compound Shape Below Is 30mm2 Calculate The Value Of X If Your Answer Is A Decimal Give It To 1 Dp class=

Sagot :

mhanifa

Answer:

  • x = 2.5 mm

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Set equation for area of given shape:

  • x*4 + x*(2x + 3) = 30

Simplify and solve for x:

  • 4x + 2x² + 3x = 30
  • 2x²+ 7x = 30
  • 2x² + 7x - 30 = 0
  • x = [-7 ± √(7² - 4*2*(-30))] /4
  • x = (-7 ± √289)/4
  • x = (-7 ± 17)/4
  • x = (10/4) and x = (- 24)/4 (discarded as negative number for the segment length)
  • x = 2.5 mm

semsee45

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:

  • w = x
  • l = 4 mm

Dimensions of the larger rectangle:

  • w = x
  • l = (2x + 3) mm

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.

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