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Ivanshal [37]
3 years ago
12

The sides of a right triangle containing the right angle are (5x) cm and (3x - 1) cm. If the area of the triangle be 60 cm, calc

ulate the length of the sides of the triangle.
Mathematics
2 answers:
ladessa [460]3 years ago
6 0

Answer: hypotenuse (h) = 17 cm

Step-by-step explanation:

Nadusha1986 [10]3 years ago
6 0

The area of a right triangle is found using the formula 1/2 x base x height.

Using the provided information the equation becomes:

60 = 1/2 * 5x * (3x-1)

Combine 1/2 and 5x:

60 = 5x/2 * (3x-1)

Multiply each term by 2/5:

24 = 3x^2 - x

Subtract 24 from each side:

3x^2 - x - 24 = 0

Now factor the polynomial:

(x-3)(3x+8) = 0

Solve for each x for 0:

3-3 = 0, so x = 3

3x +8 = 0 : subtract 8 from each side:

3x = -8

divide both sides by 3: x = -8/3

Since a side of a triangle cannot be a negative value, we now know x = 3

Now replace x in each side with 3 and solve:

5x = 5(3) = 5 x 3 = 15

3x-1 = 3(3)-1 = 9-1 = 8

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Cameron's current service charge of $0.95 per song, and the new service charge of $0.89 per song and $12 fee for joining, gives;

  • Formula for finding the number of songs that makes the cost of both services the same is; 0.95•s = 12 + 0.89•s

  • Computing the value of <em>s </em>that satisfies the above equation gives the number of songs at which the cost of both service is the same as 200 songs

  • The interpretation is the the cost of either service is the same when 200 songs are downloaded

<h3>How can the equation that gives the required number of songs be found?</h3>

To Formulate

The charges for songs on the current music service is, C1 = 0.95•s

The charges for the new download service is, C2 = 12 + 0.89•s

Where the $12 is the joining fee

When the cost is the same for both service, we have;

C1 = C2

Which gives;

  • 0.95•s = 12 + 0.89•s

The equation to represent when the cost for both service is the same is therefore;

0.95•s = 12 + 0.89•s

Computing;

The number of songs that gives the same costs is therefore;

0.95•s = 12 + 0.89•s

12 = 0.95•s - 0.89•s = 0.06•s

s = 12 ÷ 0.06 = 200

  • The number of songs at which the cost of each option will be the same is <em>s </em>= 200 songs

Interpreting the solution;

The interpretation is, the cost of songs downloaded on both service will be the same, when 200 songs are downloaded.

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