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Two ladders are leaning against a wall as shown, making the same angle with the ground. The longer ladder reaches 40 feet up the wall. Hoa far up the wall does the short ladder reach?​

Two Ladders Are Leaning Against A Wall As Shown Making The Same Angle With The Ground The Longer Ladder Reaches 40 Feet Up The Wall Hoa Far Up The Wall Does The class=

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ZhylixPhairaviz

Answer:

[tex]\large \tt { 16 \: \: \:feet }[/tex]

Step-by-step explanation:

Setting up the equation, establish the best proportion.

  • [tex]\large \tt \dfrac{x}{40}[/tex] = [tex]\large \tt \dfrac{20}{50}[/tex]

[tex]\: [/tex]

Solving the equation, setting up the ratios and then cross multiply.

  • [tex]\large \tt \dfrac{x}{40}[/tex] = [tex]\large \tt \dfrac{20}{50}[/tex]

  • [tex]\large \tt {(x)(50 \: ) = }[/tex] [tex]\large \tt {(20)(40)}[/tex]

  • [tex]\large \tt {50x \: = }[/tex] [tex]\large \tt {800}[/tex]

  • [tex]\large \tt \dfrac{50x}{50}[/tex] = [tex]\large \tt \dfrac{800}{50}[/tex]

  • [tex]\large \tt \purple {x \: = \: 16 }[/tex]

[tex]\:[/tex]

∵ Therefore, the short ladder reach the wall up to 16 feet.