Find the x and the area of the shape perimeter is 64.5

Mathematics

1 answer:

Umnica [9.8K]3 years ago

4 0

Answer:

x=8

A = 192

Step-by-step explanation:

The perimeter is the sum of the outer lengths

17.9 + 22.6 + 3x = 64.5

Combine like terms

40.5 +3x = 64.5

Subtract 40.5 from each side

40.5 +3x -40.5 = 64.5 - 40.5

3x =24

Divide each side by 3

3x/3 = 24/3

x = 8

The area of a triangle is given by

A = 1/2 bh

The base is 3x = 3(8) =24

and the height is 2x = 2(8) =16

A = 1/2 (24) * 16

A =192

You might be interested in

Given points A (-3,-4) and B (2,0), points P (-1,-12/5) partitions line AB in the ratio

kvv77 [185]

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&A&(~ -3 &,& -4~) 
&P&(~ -1 &,& -\frac{12}{5}~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
AP=\sqrt{[-1-(-3)]^2+[-\frac{12}{5}-(-4)]^2}
\\\\\\
AP=\sqrt{(-1+3)^2+(-\frac{12}{5}+4)^2}\implies AP=\sqrt{2^2+\left( \frac{8}{5} \right)^2}
\\\\\\
AP=\sqrt{4+\frac{64}{25}}\implies AP=\sqrt{\cfrac{164}{25}}\implies AP=\cfrac{\sqrt{164}}{\sqrt{25}}
\\\\\\
\boxed{AP=\cfrac{2\sqrt{41}}{5}}$

$\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
&P&(~ -1 &,& -\frac{12}{5}~) 
&B&(~ 2 &,& 0~)
\end{array}
\\\\\\
PB=\sqrt{[2-(-1)]^2+[0-\left(-\frac{12}{5} \right)]^2}
\\\\\\
PB=\sqrt{(2+1)^2+\left( \frac{12}{5} \right)^2}\implies PB=\sqrt{9+\frac{144}{25}}\implies PB=\sqrt{\cfrac{369}{25}}
\\\\\\
PB=\cfrac{\sqrt{369}}{\sqrt{25}}\implies \boxed{PB=\cfrac{3\sqrt{41}}{5}}$

so, let's check the ratio of AP:PB

$\bf AP:PB\implies \cfrac{AP}{PB}\implies \cfrac{\frac{2\sqrt{41}}{5}}{\frac{3\sqrt{41}}{5}}\implies \cfrac{2\underline{\sqrt{41}}}{\underline{5}}\cdot \cfrac{\underline{5}}{3\underline{\sqrt{41}}}\implies \cfrac{2}{3}$

7 0

3 years ago

Joey is running an experiment with a mass on a spring. Joey models the height of the mass above the table he is working on using

galben [10]

Answer: 1.8 s

Step-by-step explanation:

Given

The height of the spring mass system above the table is given by

$h(t)=6.85\cos (3.42t)+9$