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$Oppgave 3 Gitt firkanten ABCD ovenfor. a) Bestem et eksakt uttrykk for omkretsen av firkanten. b) Vis at forholdet mellom arealet av /_\ABD og arealet av /_\BCD er (3)/(2)(sqrt3+1)$

Oppgave $3$ $\newline$ Gitt firkanten $A B C D$ ovenfor. $\newline$ a) Bestem et eksakt uttrykk for omkretsen av firkanten. $\newline$ b) Vis at forholdet mellom arealet av $\triangle A B D$ og arealet av $\triangle B C D$ er $\frac{3}{2}(\sqrt{3}+1)$

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Q. Oppgave

3

\newline

Gitt firkanten

A B C D

ovenfor.

\newline

a) Bestem et eksakt uttrykk for omkretsen av firkanten.

\newline

b) Vis at forholdet mellom arealet av

\triangle A B D

og arealet av

\triangle B C D

\frac{3}{2}(\sqrt{3}+1)

Calculate Perimeter: Calculate the perimeter of the quadrilateral $ABCD$ by adding the lengths of all sides. $\newline$ Perimeter = $AB + BC + CD + DA$
Determine Side Lengths: Assume the lengths of the sides are given or can be determined from the figure (since the problem statement doesn't provide them). $\newline$ Let's say $AB = a$ , $BC = b$ , $CD = c$ , and $DA = d$ . $\newline$ Perimeter = $a + b + c + d$
Calculate Triangle Areas: For the ratio of the areas of triangles ABD and BCD, use the formula for the area of a triangle $(\frac{1}{2} \times \text{base} \times \text{height})$ . Let's say the base and height for $\triangle ABD$ are $e$ and $f$ , and for $\triangle BCD$ are $g$ and $h$ . Area of $\triangle ABD = (\frac{1}{2}) \times e \times f$ Area of $\triangle BCD = (\frac{1}{2}) \times g \times h$
Calculate Area Ratio: Calculate the ratio of the areas. $\newline$ Ratio = (Area of $\triangle ABD$ ) / (Area of $\triangle BCD$ ) $\newline$ Ratio = $\left(\frac{1}{2} \cdot e \cdot f\right) / \left(\frac{1}{2} \cdot g \cdot h\right)$
Simplify Ratio: Simplify the ratio by canceling out the common factors. $\newline$ Ratio = $(e \cdot f) / (g \cdot h)$
Substitute Given Ratio: Substitute the given ratio $(3)/(2)(\sqrt{3}+1)$ into the equation. $\newline$ $(e \cdot f) / (g \cdot h) = (3)/(2)(\sqrt{3}+1)$