The national flight museum has a model of a world

Ответ:

guadalupemarlene2001

03.01.2022

look at the picture.

$efgh\sim abcd\to2: 3$

ef : ab = 2 : 3

gf : cb = 2 : 3

gh : cd = 2 : 3

he : da = 2 : 3

∠a ≅ ∠e

∠b ≅ ∠f

∠c ≅ ∠g

∠d ≅ ∠h

$6: 3x=2: 3\to\dfrac{6}{3x}=\dfrac{2}{3}\to\dfrac{2}{x}=\dfrac{2}{3}\to2x=(2)(3)\to x=3$

use pythagorean theorem:

$a^2=8^2+(2\cdot3)^2\\\\a^2=64+36\\\\a^2=100\to a=\sqrt{100}\to a=10\ cm$

the length of the abcd trapezoid sides:

|ab| = 3 cm

|bc| = 10 cm

|cd| = 3(3) cm = 9 cm

|da| = 8 cm

the perimeter of abcd = 3 + 10 + 9 + 8 = 30 cm

the ratio of perimeters of the tarapezoids is equal 2 : 3.

$p_{efgh}: p_{abcd}=2: 3\to\dfrac{p_{efgh}}{p_{abcd}}=\dfrac{2}{3}$

substitute:

$\dfrac{p_{efgh}}{30}=\dfrac{2}{3}$ cross multiply

$3p_{efgh}=(30)(2)$ divide both sides by 3

$p_{efgh}=20\ cm$

$p_{abcd}=30\ cm\\\\p_{efgh}=20\ cm$

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