The sum of the lengths of the two legs of a right angle is 34 meters.?

Question

The sum of the lengths of the two legs of a right triangle is 34 meters. If the length of the hypotenuse is 26 meters find the length of each leg. help!!!

Answer 1

a² + b² = (26)²

a+b = 34
a = 34 - b

(34-b)² + b² = (26)²

(34)² -68b +b² + b² = (26)²
1156 - 68b + 2b² = 676
2b² -68b + 480 = 0
b² -34b + 240 = 0
(b-24)(b-10) = 0

Sides a and b are 10 and 24 meters long

Answer 2

a² + b² = c²

In this case:

b = 34 - a

So:

a² + (34 - a)² = 26² { Substitute for b }

a² + 1156 - 68a + a² = 676 { Expand (34 - a)² }

2a² - 68a + 480 = 0 { Combine like terms }

a² - 34a + 240 = 0 { Divide everything by 2 }

(a - 24)(a - 10) = 0 { Quadratic Formula }

a = 24 or 10 { Possible values for a }

b = 10 or 24 { Possible values for b }

So, the two sides of your triangle are 10 meters and 24 meters.

Answer 3

Using the pythagorean theorem
a² + b² = c²

Let x be one leg, the other 34 - x

x² + (34 - x)² = 26²

x² + 1156 - 68x +x² = 676

2x² - 68x+ 480 = 0

divide thru by 2

x² - 34x +240 = 0

(x - 10)(x - 24) = 0

x = 10, x = 24

The two sides are 24 and 10
.

Answer 4

Let one of the legs be x m long, so the other one is (34 - x) m.

Since it`s a right angled triangle, then using Pythagoras` Theorem:

x^2 + (34 - x)^2 = 26^2

You now solve this equation for x.

Hope this helps, Twiggy.

Answer 5

let 2 legs be a &b
sum of 2 legs is a+b=34
b=34-a

let hypotenuse be c
c=26


c^2 = a^2+ b^2

(26)^2 = a^2+(34-a)^2
676=a^2+1156+a^2-68a
676-1156=2a^2-68a
-480=2a^2-68a
-240 =a^2-34a
0=a^2-34a+240
0=a^2-24a-10a+240
0=a(a-24)-10(a-24)
0=(a-24)(a-10)
a= 24 or 10

if a =24
then
b= 34-a
b=34-24
b=10

if a =10
then
b=34-a
b=34-10
b=24

the length of 2 legs = 10 & 24

Answer 6

a - squared + b - squared = C - Squared.

axa + bxb = 26x26

axa + bxb = 676

What 2 numbers add up to 34 that when squared add up to 676.

the sides are 10m and 24 m

10x10 = 100
24x24 = 576

100+576 = 676

Answer 7

You have been given two equations:
1) a+b=34
2) c=26
Now just remember that the Pythagorean Theorem gives you a third equation. With three equations and three unknowns you should have enough information for a solution.