The sides 2

The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.

Correct answer:

h =  14
o =  70

Step-by-step explanation:

$$\begin{gathered} a:b:c:d=2:5:8:5 \\ a=8x \\ b=d=5x \\ c=2x \\ a\mathrm{\mid }\mathrm{\mid }c \\ S=245 \\ h=\sqrt{d^2-((a-c)\mathrm{/}2{)}^2} \\ h=x\cdot \sqrt{5^2-((8-2)\mathrm{/}2{)}^2} \\ h=x\cdot \sqrt{5^2-((8-2)\mathrm{/}2{)}^2} \\ h=x\cdot \sqrt{16} \\ h=4x \\ S={\displaystyle \frac{a+c}{2}}h \\ S={\displaystyle \frac{8x+2x}{2}}h \\ S={\displaystyle \frac{8x+2x}{2}}\cdot 4x \\ S=5x\cdot 4x \\ x=\sqrt{S\mathrm{/}20}=\sqrt{245\mathrm{/}20}={\displaystyle \frac{7}{2}}=3\frac{1}{2}=3.5 \\ h=4\cdot x=4\cdot 3.5=14 \end{gathered}$$

$$\begin{gathered} a=8\cdot x=8\cdot 3.5=28 \\ b=5\cdot x=5\cdot 3.5={\displaystyle \frac{35}{2}}=17\frac{1}{2}=17.5 \\ d=5\cdot x=5\cdot 3.5={\displaystyle \frac{35}{2}}=17\frac{1}{2}=17.5 \\ c=2\cdot x=2\cdot 3.5=7 \\ {S}_1={\displaystyle \frac{a+c}{2}}\cdot h={\displaystyle \frac{28+7}{2}}\cdot 14=245 \\ {S}_1=S \\ o=a+b+c+d=28+17.5+7+17.5=70 \end{gathered}$$

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