how do you find right triangle other two sides if you know length of hypotenuse is 18 and perimeter is 40?

Question

right-angled triangle is required with the hypotenuse of length 18m .if the perimeter of triangle is 40m. determine the lengths of the other two sides.

Answer 1

Let x and y be the other two sides

18 is hypotenuse
=>x<18,y<18

x+y+18=40
x+y=22------------------1

x^2+y^2=(18)^2=324----------2------Pythagoras theorem

x^2+(22-x)^2=324---------------------Put 1 in 2

Simplify,
x^2 + 484 -44x +x^2=324

2 x^2 - 44x +160 =0

x^2 -22x +80=0

Solve to get x,
only 1 of two value is possible
(Other is discarded if<0 or >18
or will be y value if 2 values add up to 22).

Answer 2

11. what's the gap between (-a million, -3) and (2,3)? distance = sqrt[(3-(-3))^2 + (2-(-a million))^2] = sqrt[6^2 + 3^2] = sqrt[36+9] = sqrt[40 5] = 3sqrt(5) answer: a) 3?5 17. One leg of a perfect triangle is 15. The hypotenuse is 17. what's the fringe of the triangle? enable b = the option aspect of the triangle enable a = the adjacent aspect of the triangle enable c = the hypotenuse aspect of the triangle by Pythagorean Theorem, we've: 15^2 + b^2 = 17^2 225 + b^2 = 289 b^2 = sixty 4 b = 8 the fringe of the triangle = a + b+ c = 15 + 8 + 17 = 40 answer: b) 40 19. aspect: 5x^2 – 13xy – 6y^2 (5x + 2y)(x - 3y) answer: b) (5x+2y)(x-3y) 21. a deliver cruises downstream for 2 hours previously heading decrease back. It takes 3.5 hours going upstream to get decrease back. If the speed of the flow is 8 mph, what's the speed of the boat in nevertheless water? enable x = % of the boat in nevertheless water (x-8)3.5 = 2(x+8) 3.5x - 28 = 2x+16 a million.5x = 40 4 x = 29 a million/3 answer: d) 29.3 mph substantial be conscious: the gap that the boat traveled cruising downstream and the gap that the boat traveled cruising upstream to get decrease back is an similar. even as the boat travels downstream, the flow % 8 mph is further to the boat's %. even as the boat travels upstream, the flow % 8 mph is subtracted from the boat's %. 24. At what element do the strains y = 4x + 7 and y = -4x – 11 intersect? 4x + 7 = -4x - 11 8x = -18 x = -9/4 y = 4(-9/4) + 7 y = -2 answer: c) (-9/4, -2) Somu and that i found out situation 21 with out helping one yet another. :D

Answer 3

If the perimeter is 40 and the hypotenuse has length 18, the other two sides must have lengths totalling 22.

Call the length of one side x. The length of the other side is 22 - x.

Now use the Pythagorean Theorem:

x^2 + (22 - x)^2 = 18^2

x^2 + 484 - 44x + x^2 = 324

2x^2 - 44x + 160 = 0

x^2 - 22x + 80 = 0

Use the Quadratic Formula:

x = [-b +/- sqrt(b^2 - 4ac)]/2a

x = 22 +/- sqrt(484 - 320)]/2

x = [22 +/- sqrt(164)]/2

x = 22 +/- 2*sqrt(41)]/2

x = 11 +/- sqrt(41)

x is approximately 17.40 or 4.60

As it turns out, if one of the above solutions is one side, the other solution is the other side. This means that there is only one unique solution.

The triangle has side lengths of 4.60 and 17.60 (approximately).

The exact answers are 11 + sqrt(41) and 11 - sqrt(41).

Answer 4

Think about the three sides of a triangle

18 (the hypotenuse), x (the opposite leg) and y (the adjacent leg)

Since you've a right-angled triangle,
x / y = 18 . You already know that its perimeter
is 40, then you've x + y + 18 = 40 .

Now, you need only to replace x or y in one of the
equations.

I tried to draw a triangle but it didn't fit.
Hope I can help you.

Answer 5

if the other two sides are a and o
then,
a + o = 40 - 18 = 22 -------(1)
a^2 + o^2 = 18^2 -------(2)

squaring 1,
a^2 + 2ao + o^2 = 22^2
=> 2ao = 22^2 - 18^2 , by 2
then 2ao = (22+18) (22-18) , by using the difference of two squares.
2ao = 160
a = 80/o

in 1,

80/o + o = 22
multiply throughout by o and solve the quadratic in o, the answer is the positive one.
then plug the obtained value back in 1 for a.

hope this helps!

Answer 6

Let x , y and p be the two sides and perimeter, respectively. Then:
x+y+18=40
x+y=22
y=22-x ---(1)
x^2+y^2= 18^2---(2)
Insert (1) into (2) and solve for x
x^2+(22-x)=18^2
x=17.6 or x=4.6 and hence y=4.6 ory=17.4, respectively.
Therefore the two sides are 17.4 and 4.6 units.

Answer 7

let the legsbe xand y
x+y=40-18=22
x=22-y
x^2+y^2=18^2
(22-y)^2+y^2=324
484-44t+y^2+y^2=324
2y^2-44t+160=0
dividing by 2
y^2-22t+80=0 solve for y and substitute to getx

Answer 8

let the other two sides have length x and y cm. then
X+Y+18=40
18square - Y square =X square
solve equations!

Answer 9

24 M

Answer 10

Seriously i don't get your english
But from what i comphrehend,

remaining angle of Right angle triangle(180-90)/2
The right angle is 90 deg and the 2 other equal side are of 45deg each.

since hypotenuse=90deg

(Sin90/18cm)=(sin45/xcm)

step 1:find (sin90/18cm)
once u have the answer,we denote the answer as "Y"

Take (sin45/Y)=xcm