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Mazyrski [523]
2 years ago
5

Two ladders are leaning against a building, forming two similar triangles as shown below. The top of the longer ladder is 28 fee

t up the building's side. The top of the shorter ladder is 20 feet up the building's side and its base is 15 feet from the bottom of the building. What is the length of the longer ladder?
Mathematics
1 answer:
postnew [5]2 years ago
7 0

Answer:

The length of the longer ladder is 35 ft

Step-by-step explanation:

Please check the attachment for a diagrammatic representation of the problem

We want to calculate the length of the longer ladder ;

We make reference to the diagram

Since the two right triangles formed are similar. the ratios of their sides are equal;

Thus;

20/15 = 28/x + 15

20(x + 15) = 15(28)

20x + 300 = 420

20x = 420-300

20x = 120

x = 120/20

x = 6

So we want to calculate the hypotenuse of a right triangle with other sides 28ft and 21 ft

To do this, we use the Pythagoras’ theorem which states that square of the hypotenuse equals the sum of the squares of the two other sides

Let the hypotenuse be marked x

x^2 = 28^2 + 21^2

x^2 = 1,225

x = √1225

x = 35 ft

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7 0
2 years ago
LCM of two numbers is 1134 and HCF is 18. if one of the numbers is 162, find the other. number.<br>​
Brilliant_brown [7]
<h3>Answer:  126</h3>

=====================================================

Work Shown:

Let x and y be the two numbers.

We're given x = 162 and the variable y is unknown.

We're also given LCM = 1134 and HCF = 18

So,

LCM = (x*y)/HCF

1134 = 162*y/18

1134 = (162/18)y

1134 = 9y

9y = 1134

y = 1134/9

y = 126

The other number is 126

---------------------

Notice that

  • 162 = 18*9
  • 126 = 18*7

showing that 18 is the highest common factor (HCF) of the numbers 162 and 126. This partially confirms the answer.

Now let,

  • A = multiples of 162
  • B = multiples of 126

So,

  • A = 162, 324, 486, 648, 810, 972, 1134, 1296, ...
  • B = 126, 252, 378, 504, 630, 756, 882, 1008, 1134, 1260, ...

We see that 1134 is in each list of multiples and the smallest such common item. So the lowest common multiple (LCM) of 162 and 126 is 1134. This helps fully confirm the answer.

7 0
2 years ago
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