Question

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 1

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

Answer 2

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`\large \sf \underline{Problem:}`

• 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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`\large \sf \underline{Answer:}`

`\huge \sf \qquad \quad{ 16 \: feet }`

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`\large \sf \underline{Solution:}`

Setting up the equation, establish the best proportion.

`\large : \implies\qquad\large \sf(x)/(40) =\large\sf (20)/(50)`

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

• 
  `\qquad\large \sf(x)/(40) = \large \sf (20)/(50)`

• 
  `\qquad\large \sf{(x)(50 \: ) = } \large \sf {(20)(40)}`

• 
  `\qquad\large \sf{50x \: = 800 }`

• 
  `\qquad\large \sf(50x)/(50) = \large \sf(800)/(50)`

• 
  `\qquad\large \sf{ \underline{ \underline{\pmb {x \: = \: 16 }}}}`

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

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