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Colt1911 [192]
3 years ago
6

The shortest leg of a triangle is 1 feet shorter than the other leg.The hypotenuse of this triangle is 5 feet. what are the leng

ths of the two legs of this triangle?
The shortest leg is_____ ft long


The other leg is ________ft long
Mathematics
2 answers:
givi [52]3 years ago
7 0

Answer:

  • shortest: 3 ft
  • other: 4 ft

Step-by-step explanation:

The right triangle with hypotenuse 5 that has legs that differ by 1 is the 3-4-5 right triangle. The legs are 3 ft and 4 ft.

__

<em>Alternate solution</em>

If you have never heard of a 3-4-5 right triangle, you can figure the leg lengths algebraically using the Pythagorean theorem. Let x represent the length of the "other" leg. Then the shortest is (x-1). The Pythagorean theorem tells you ...

  5^2 = (x)^2 +(x -1)^2

  25 = 2x^2 -2x +1

  12 = x^2 -x = x(x -1)

Factors of 12 that differ by 1 are 3 and 4 or -3 and -4. We want x to be positive, so the value of interest is x=4

The "other" leg is 4 ft; the shortest leg is 3 ft.

GuDViN [60]3 years ago
4 0

Answer:

3 ft, 4 ft

Step-by-step explanation:

Represent the length of the shortest leg using x.  Then the other leg length is x + 1.  Applying the Pythagorean Theorem,

x^2 + (x + 1)^2 = 5^2, or

x^2 + x^2 + 2x + 1 = 25, or

2x^2 + 2x - 24 = 0.

Reducing this, we get x^2 + x - 12 = 0, or (x + 4)(x - 3) =0.

Solving for x:  x + 4 = 0 => x = -4; also x - 3 = 0 => x = 3

Since we're measuring length, let's omit x = -4 and focus on x = 3.

Shortest leg is 3 ft long; other leg length is 3 + 1 ft, or 4 ft, long.

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Step-by-step explanation:

4-7 equals -3

-1-4 equals -5

Cancel out the negatives which makes a positive

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76 + 4 is 80... don't know what you're asking
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The two dot plots show the number of guests per night.
LiRa [457]

A dot plot or for chart is a statistical plot consisting of data points that are plotted on a scale using dots.

<h3>What is a dot plot?</h3>

Your information is incomplete. Therefore, an overview of a dot plot will be given. A dot plot is a data visualization where the day points are plotted as dots on the graph.

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7 0
2 years ago
Read 2 more answers
Un mester popular a confectionat intru-n an 480 de fluiere,ocarine si viori.Cate instrumente de fiecare fel a confectionat meste
Marta_Voda [28]

Answer:

138 fluiere, 158 ocarine, 184 viori

Step-by-step explanation:

given:

(1) fluiere + ocarine +viori = 480

(2) fluiere + ocarine =296

(3) ocarine + viori =342

din ecuatia (3) avem: viori= 342-ocarine

din ecuatia(2) avem : fluiere= 296-ocarine

in ecuatia (1) inlocuieste ce ai gasit ca sa fie o ecuatie doar cu necunoscuta ocarine: fluiere + ocarine +viori = 480

296-ocarine +ocarine+ 342-ocarine  =480

296+342-480 = ocarine =158

viori = 342-158 = 184

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8 0
2 years ago
The parents' club will need 100 of the same item for international night. They have a budget of $250. The choices are 100 baseba
Nuetrik [128]

Answer:

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

Step-by-step explanation:

Given:

Item to be bought = 100

Total Budget = $250

Cost of each Baseball Hat = $2.45

Cost of each sports bottles = $2.50

Cost of each flag = $2.75

We need to find which items can they afford to buy.

Solution:

each Baseball Hat = $2.45

100 Baseball Hat = Cost of 100 Baseball Hat

Using Unitary method we get;

Cost of 100 Baseball Hat  = 2.45\times 100 =\$245

each sports bottles = $2.50

100 sports bottles = Cost of 100 sports bottles

Using Unitary method we get;

Cost of 100 sports bottles  = 2.5\times 100 =\$250

each flag = $2.75

100 flags = Cost of 100 flags

Using Unitary method we get;

Cost of 100 flags  = 2.75\times 100 =\$275

Hence from above we can see that;

Cost of 100 Base ball hat and 100 sports bottles are within the budget while Cost of 100 flags exceed the budget.

So we can say that;

The parents' club can afford to buy 100 Baseball hats or 100 sports bottles.

6 0
2 years ago
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