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ANSWER THIS WITH EXACT SOLUTION!.

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. How far up the wall does the short ladder reach?​

ANSWER THIS WITH EXACT SOLUTIONTwo ladders are leaning against a wall as shown making the same angle with the ground The longer ladder reaches 40 feet up the wa class=

Respuesta :

for example, l is the length of short ladder we want to find

Make a comparison

ladder/wall height = ladder/wall height

l/20 = 50/40

l/20 = 5/4

l = 5/4 × 20

l = 100/4

l = 25

The short ladder is 25 ft

Therefore, The short ladder is 25 ft

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[tex] \large \sf \underline{Problem:}[/tex]

  • 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. How far up the wall does the short ladder reach?

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[tex] \large \sf \underline{Answer:}[/tex]

[tex]\huge \sf \qquad \quad{ 16 \: feet }[/tex]

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[tex] \large \sf \underline{Solution:}[/tex]

Setting up the equation, establish the best proportion.

[tex] \large : \implies\qquad\large \sf\dfrac{x}{40} =\large\sf \dfrac{20}{50} [/tex]

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

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

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

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

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

  • [tex] \qquad\large \sf{ \underline{ \underline{\pmb {x \: = \: 16 }}}}[/tex]

Hence, the short ladder reach the wall up to 16 feet.

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