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The hypotenuse of a right triangle is 6 cm and one side is 2 cm longer than the other side. Find the length of each side to one

MA_775_DIABLO [31]

Answer:

The two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

Step-by-step explanation:

Let x be one leg of the right triangle.

Since the other leg is two centimeters longer, it can be represented by the expression:

$x + 2 \text{ cm}$

According to the Pythagorean Theorem, for a right triangle:

$a^2 + b^2 = c^2$

Where c is the hypotenuse and a and b are the two legs.

The hypotenuse is given to be 6 cm and the two legs are x and (x + 2). Hence:

$(x)^2 + (x+2)^2 = 6^2$

Solve for x. Simplify:

$x^2 + (x^2 + 4x + 4) = 36$

Simplify:

$2x^2 + 4x + 4 = 36$

Subtract:

$2x^2 + 4x - 32 =0$

Divide:

$x^2 + 2x - 16 = 0$

The equation is not factorable, so we can consider using the quadratic formula:

$\displaystyle x = \frac{-b\pm\sqrt{b^2 -4ac}}{2a}$

In this case, a = 1, b = 2, and c = -16. Substitute:

$\displaystyle x= \frac{-(2)\pm\sqrt{(2)^2-4(1)(-16)}}{2(1)}$

And evaluate:

$\displaystyle \begin{aligned}x &= \frac{-2\pm\sqrt{68}}{2} \\ \\ &= \frac{-2\pm\sqrt{4\cdot 17}}{2} \\ \\ &= \frac{-2\pm2\sqrt{17}}{2} \\ \\ &= -1 \pm \sqrt{17} \end{aligned}$

Hence, our two solutions are:

$\displaystyle x = -1 + \sqrt{17} \approx 3.1\text{ or } x = -1 - \sqrt{17} \approx -5.1$

Lengths cannot be negative, so we can ignore the second solution.

Hence, the value of x or the first side length is about 3.1 centimeters.

Since the other side length is two centimeters longer, the other side is about 5.1 centimeters.

In conclusion, the two legs of the right triangle are approximately 3.1 cm and 5.1 cm and the hypotenuse is 6 cm.

4 0

3 years ago

A real word problem that uses perpendicular.

BaLLatris [955]

One common example of perpendicular lines in real life is the point where two city roads intersect. When one road crosses another, the two streets join at right angles to each other and form a cross-type pattern. Perpendicular lines form 90-degree angles, or right angles, to each other on a two-dimensional planeOther real-world examples of perpendicular lines include graph paper, plaid patterns on fabric, square lines of floor tiles, lines of mortar on brick walls, the intersecting lines of a Christian cross, metal rods on the cooking surface of a barbecue grill, wooden beams in the wall of a house, and the designs on country flags such as Norway, the United Kingdom, Switzerland, Greece, Denmark and Finland. Perpendicular lines form the corner of squares and rectangles in various real-world shapes.Perpendicular lines create four right angles at their intersection point, making 360 degrees total. Perpendicular lines also form one angle of a right triangle. Perpendicular lines are concepts taught in algebra and geometry as students learn to calculate slopes of lines on graph paper.Parallel lines differ from perpendicular lines in that parallel lines never intersect. Real-world examples of parallel lines include railroad tracks, stripes on the American flag, power lines hung between poles, lines on composition paper and plugs at the end of electrical cords..

6 0

4 years ago

Read 2 more answers

Val rented a bicycle while she was on vacation. She paid a flat rental fee of f dollars, plus $8.50 each day. The total cost at

damaskus [11]

The question is incomplete. Here is the complete question:

Val rented a bicycle while she was on vacation. She paid a flat rental fee of f dollars, plus $8.50 each day. The total cost at the end of her vacation was t dollars. Let d represent the number of days Val rented the bicycle. Write an equation representing the total cost at the end of her vacation.

Answer:

$t=f+8.5d$

Step-by-step explanation:

Given:

Flat rental fee = $f$

Variable fee per day = $8.50

Total cost at the end vacation = $t$

Number of days of her vacation = $d$

Using unitary method, we can find the variable fee for 'd' days.

1 day variable fee = $8.50

Therefore, 'd' days variable fee = $8.50d$

Total cost at the end of her vacation can be obtained by adding the fixed rental fee and the variable fee obtained for the given number of days.

Now, total cost is given as:

Total cost = Flat rental fee + Variable fee

Substituting all the variables and framing above in the form of an equation, we get:

$t=f+8.5d$

Therefore, the equation representing the total cost at the end of her vacation is $t=f+8.5d$

7 0

3 years ago

How to divide a whole number by a fraction khan academy?

mel-nik [20]

How to divide a whole number by a fraction...

example : 6 / (1/4)....when dividing with fractions, " flip " what u r dividing by, then multiply

6 * 4/1....if u have to, 6 is the same as 6/1
6/1 * 4/1 = 24/1 = 24

another example :
2 / (1/3) =
2/1 * 3/1 =
6/1 = 6

just remember to flip what u r dividing by and not the other number.

8 0

3 years ago

If the total manufacturing cost is $40000 and the total amount of units manufactured is 500 units, then the price per unit is

mezya [45]

Answer:

Unitary cost= $80

Step-by-step explanation:

Giving the following information:

Total manufacturing cost= $40,000

Number of units= 500

To calculate the unitary cost, we need to use the following formula:

Unitary cost= Total manufacturing cost / number of units

Unitary cost= 40,000 / 500

Unitary cost= $80

6 0

3 years ago