Question

37. If the sum of the sides of a right triangle is 49 inches and the hypotenuse is 41
inches, find the two sides.​

Answer 1

Answer:

if x = 9, y = 40

else if x = 40, y = 9

Step-by-step explanation:

Let x  be the length of 1 of the missing sides.

⇒49 − x  is the length of the other missing side.

Now, using pythagoras theorem,

x² + (49-x)² = 41²

x² + 2401 - 98x + x² = 1681

x² - 49x + 360 = 0

(x-9)(x-40) = 0

⇒ x = 9 or x = 40

let y = 49-x,

if x = 9, y = 40

else if x = 40, y = 9

Answer 2

Answer:

Let 'a' and 'b' be the lengths of the two shorter sides.

The sum is L + b = 49 .

So,a=49-b

Using the Pythagorean Theorem:

Perpendicular? + Base = hypotenuse

(49-b)2 + b²=412 (by substitution)

2401 - 98b + b ^ 2 + b ^ 2 = 1681

2b²-98b+720 = 0 (take 2 common from L.H.S)

b ^ 2 - 49b + 360 = 0

(b * 9)(b - 40) = 0

b=9 or b=40.

In this case, either solution will do. fb = 9 then a -49-b-49-9-40.

9rifb = 40 then a = 49-b=49-40=9. Thus, one side is 40 inches long, and the other side is 9 inches long.