the hypotenuse of a right triangle is 17cm.other side of triangle is 7cm longer than other side.find the other

Answer 1

The Pythagorean Theorem:
a^2+b^2=c^2
a^2=x
b^2=x+7
c^2=17

x^2+(x+7)^2=17^2
x^2+x^2+14x+49=289
2x^2+14x-240=0
2(x^2+7x-120)=0
x^2+7x-120=0
(x-8)(x+15)=0
x=8
7+8=15

The other sides are 8 cm. and 15 cm.

Answer 2

h = 17
b =a+7
a^2 + b^2 = h^2

a^2 +(a+7)^2 =17^2
a^2 +a^2 +14a +49 =17^2
2a^2 +14a - 240 = 0
a^2 +7a -120 =0
(a +15)(a-8) = 0
a = -15 (irrelevant to this problem
a =8 cm this is the length of the missing side
b = 15 cm

Answer 3

*The hypotenuse is the longest side of a triangle, represented by c^2

*Algebraic Expressions:

1) x
2) x+7
3) 17

*Use the Pythagorean Thereom which is, a^2 + b^2 = c^2

First: replace the terms with the corresponding variables.

a^2 + (x+7)^2 = 17^2

a^2+(x+7)(x+7) = 17*17

Sec: eliminate parenthesis - use the Foil Method.

x^2+(x)(x)+(x)(7)+(7)(x)+(7)(7)=17*17

x^2+x^2+7x+7x+49 = 289

x^2+x^2+14x+49 = 289

2x^2+14x+49=289

Third: set the equation to "0" - subtract 289 from both sides (when you move a term to the opposite side, always use the opposite sign).

2x^2+14x+49-289=289-289
2x^2+14x-240=0

Fourth: factor....find the greatest common factor.

2(x^2+7x-120)=0

*Factor the expression...multiply the 1st & 3rd term to get
-120. find two numbers that give you -120 when multiplied & 7 (2nd term) when added/subtracted. the numbers are
(15 & -8).

*With 4 terms, group "like" terms & factor both sets of parenthesis.

(x^2 + 15x) - (8x - 120) = 0
x(x+15) - 8(x+15) = 0
(x+15)(x-8) = 0

Now, you have 2(x+15)(x-8) = 0

Fifth: solve the "x" variables - set both parenthesis to "0"

a. x+15 = 0 (subtract 15 from both sides)
x = - 15

b. x - 8 = 0 (add 8 to both sides)
x = 8


Now, we can't use -15 but, we can use 8. Replace 8 with the "x" variables in the algebraic expressions.

1) 8
2) x+7 = 8+7
= 15

The other sides equal 8 and 15.

Answer 4

pythagorean theorem: 17^2=x^2+(7+x)^2
so 289=2x^2+49+14x =>
2x^2+14x-240=0

x=(-14+46)/4 we reject the negative root (x=length)
hence, x=8 the one side x+7=15 the other one

Answer 5

let one side be a
then other side is a+7
but according to pythogarus theorem,
hyp^2=sum of squares of other sides
289=a^2+(a+7)^2
a^2+(a^2+14a+49)=289
2a^2+14a-240=0
a^2+7a-120=0
a^2+15a-8a-120=0
a(a+15)-8(a+15)=0
(a+15)(a-8)=0
a=-15 or a=8
since side cannot be negative,
the right answers is a=8

therefore the other sides are 8cm and 15cm.

Answer 6

the sides are 8 15 and 17
its a Pythagorean triple

Answer 7

Given:
c = 17
a = x + 7
b = x
Use the Pythagorean Formula: a² + b² = c²
Solve for x:
(x + 7)² + x² = (17)²

Answer 8

15 cm

Answer 9

a squared + b squared = c squared

1. You take the 2 sides that you use to find the hypotonuse.

2. You take those to sides squared and the add them to- gether.

3. Find the square root of the answer and you have YOUR answer!

Hope that I helped!

Answer 10

use pythagorean theorem a2+b2=c2
17(17)=289
7(7)=49
289-49=240
therfore the other side is 15.491933
you take the square root of 240 is how you get the answer