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3 years ago

If the length of a leg of a triangle is 39.2 and the area of the triangle is 63 what is the length of the other leg

Mathematics

1 answer:

Nadya [2.5K]3 years ago

7 0

Answer:

The length of the other leg is $3.21\ units$

Step-by-step explanation:

I will assume that the triangle is a right triangle

In a right triangle the legs are perpendicular

The area of a right triangle is equal to

$A=\frac{1}{2}(a)(b)$

where

a and b are the legs of the triangle

In this problem we have

$a=39.2\ units$

$A=63\ units^{2}$

substitute the values

$63=\frac{1}{2}(39.2)(b)$

$126=(39.2)(b)$

$b=126/(39.2)=3.21\ units$

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Out triangle-shaped pennants on the first day of school. If each pennant has a base of 5 inches and a height of 12 inches, what

brilliants [131]

Answer:

Area of the penny = 30 square inches

Step-by-step explanation:

Out triangle-shaped pennants on the first day of school. If each pennant has a base of 5 inches and a height of 12 inches, what is the area of each pennant in square inches?

The pennant is triangular in shape. Hence:

Area of a Triangle = 1/2× Base × Height

Base of the pennant = 5 inches

Height = 12 inches

Area of the pennant = 1/2 × 5 inches × 12 inches

= 30 square inches

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2 years ago

a ladder 30 decimeters long is leaning against the side of a building. the ladder makes an angle of 25 degrees with the side of

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H=how far up from the ground does the ladder touch the building
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Answer: The height that the ladder touch the building far up from the ground is 12.7 decimeters.

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3 years ago

Which fraction represents the decimal 0. ModifyingAbove 1 2 with Bar? One-twelfth StartFraction 3 Over 25 EndFraction StartFract

mestny [16]

The considered decimal number is expressed by the fraction given by: Option C: 4/33

<h3>How to convert from decimal to fraction?</h3>

For conversion from decimal to fraction, we write it in the form a/b such that the result of the fraction comes as the given decimal. Usually, to get the decimal of the form a.bcd, we count how many digits are there after the decimal point (if its finite), then we write 10 raised to that many power as denominator, and the considered number without any decimal point as numerator.

For example:

$0.99 = \dfrac{99}{10^2} = \dfrac{99}{100}$

(10 raised to power k = 1 followed by k zeroes)

<h3>What is the sum of an infinite geometric series?</h3>

The sum of an infinite geometric series having the initial term "a" and the multiplication per term is done by "r" such that r < 1

is given by

$S_{\infty} = \dfrac{a}{1-r}$

The series would look like $a+ ar+ ar^2+\cdots$

For the considered case, the given decimal number is

$0.\overline{12} = 0.121212\cdots$

We can check all the options available one by one, so as to know which one ends up giving this pattern, or we can use another technique as shown below.

$0.12121... = (0.1 + 0.001 + 0.00001 + ... ) + (0.02 + 0.0002 + 0.000002 + ... )$

Each of the two series obtained are geometric series with the multiplication factor as 1/100

Using the sum formula for evaluation of an infinite geometric series, and the fact that initial term of first series is 0.1 and that of second series is 0.02, we get:
$0.121212... = \dfrac{0.1}{1-1/100} + \dfrac{0.02}{1 - 1/100} = \dfrac{1}{99/100}(\dfrac{1}{10} + \dfrac{2}{100})\\0.121212... = \dfrac{100}{99}\times(\dfrac{10}{100} + \dfrac{2}{100})\\\\\\0.121212 ... = \dfrac{12}{99} = \dfrac{4}{33}$