Mathematics, 25.07.2021 01:00 TheViperMlg23676

The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side lengths of the right triangle given the perimeter= 60 and it's area= 120

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Answer from: nikolas36

9514 1404 393

10 and 24

Step-by-step explanation:

We know that some of the Pythagorean triples that appear in math problems are (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17).

These have (perimeter, area) values of (12, 6), (30, 30), (56, 84), (40, 60).

For some scale factor n, we want (p·n, a·n²) = (60, 120). Of the triangles listed, we see that the (5, 12, 13) triangle scaled by n=2 will satisfy the problem requirements. (30·2, 30·2²) = (60, 120)

The side lengths are 10 and 24.

Check

For the side lengths we found, the perimeter is 10+24+26 = 60; the area is 1/2(10)(24) = 120. The hypotenuse is 2×13 = 26 = 24+2.

In the attached, one side is x, the other is y. The hypotenuse is (x+2). The square root equation comes from ...

x² +y² = (x+2)² ⇒ y² = (x² +4x +4) -x² ⇒ y² = 4x +4 = 4(x +1)

_____

Additional comment

The graph shows the solution of the various constraints. At least, the combination of constraints will give a quadratic equation in x. They can be combined in a way that gives a cubic equation in x. Either way, we prefer the graphical or "guess and check" approach (above) as being easier to do.

Using the third equation in the attachment to write an expression for y, we have ...

y = 58 -2x

Substituting that into the second equation gives ...

(x(58 -2x)/2 = 120

29x -x² = 120

x² -29x +120 = 0

(x -5)(x -24) = 0 . . . . x = 5 or 24.

The root x=5 is a legitimate solution to the pair of equations we chose to solve. The line y=58-2x intersects the hyperbola xy/2 = 120 in two places. However, (x, y) = (5, 48) does not satisfy the hypotenuse requirement that x+2 > y.

The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side len

Answer from: Quest

answer

$25\pi {ft}^{2}$

explanation

the area of a circle is calculated using the formula

$area =\pi {r}^{2}$

$area = \frac{\pi \: {d}^{2} }{4}$

we can use any of the above formulae to calculate the required. preferably, let us use the latter since the diameter is

$d = 10ft$

we substitute the diameter into the formula to get:

$area = \frac{\pi \: \times {10}^{2} }{4}$

$area = \frac{100\pi}{4}$

$area = 25\pi {ft}^{2}$

this is the exact value for the area of the circle.

the correct answer is a

1. 25pi ft^2 2. 5pi ft^2 3. 10pi ft^2 3. 20pi ft^2

Answer from: Quest

1.677

step-by-step explanation:

i'm not good at explaining stuff but if you need an answer i'm here for you.

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The hypotenuse of a right triangle is two more than the length of one of its legs. Find the side len...