anonymous
  • anonymous
done
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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ybarrap
  • ybarrap
Ok. Let's start.
ybarrap
  • ybarrap
#17
ybarrap
  • ybarrap
How can we find "x"? |dw:1377642805163:dw|

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ybarrap
  • ybarrap
Use Pyhagora's Theorem: \( 5^2=3^2+x^2\). Now what is \(x\)?
ybarrap
  • ybarrap
\( x=\sqrt{5^2-3^2}\). Now what's \(x\)?
ybarrap
  • ybarrap
\( x=\sqrt{25-9}=\sqrt{16}\)
ybarrap
  • ybarrap
Sure. We will first determine \(x\) then determine the area of the triangle, then the area of the rectangle. We'll sum the two areas to get the total area. Here is how we determined \(x\):
ybarrap
  • ybarrap
$$ x^2 +3^25^2\\ x^2 =5^2-3^2\\ x=\sqrt{5^2-3^2}\\ x=\sqrt{16}\\ x=4\\ $$ Now the area of the triangle:
ybarrap
  • ybarrap
Area of triangle is \(\dfrac 1 2bh\), where \(b\) is base and \(h\) is height. $$\Large A_{triangle}=\dfrac 1 2 \times x \times3\\ \Large A_{triangle}=\dfrac 1 2 4\times3\\ \Large A_{triangle}=2\times3=6\\ $$ This is the area of the triangle. Next, the area of the rectangle:
ybarrap
  • ybarrap
Area of a rectangle is \(l\times w\), where \(l\) is length and \(w\) is width. $$ \Large A_{rectangle}=l\times w\\ \Large A_{rectangle}=l\times x\\ \Large A_{rectangle}=6\times 4\\ \Large A_{rectangle}=24\\ $$ Now we have the areas of the rectangle and the triangle. We now just need to sum them: $$ \Large Total~Area=A_{triangle}+A_{rectangle} $$
ybarrap
  • ybarrap
@MayMay_69
ybarrap
  • ybarrap
@MayMay_69

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