The longer leg of a right triangle is 1 m longer than the shorter leg. The hypotenuse is 9 m longer than the shorter leg. Find the side lengths of the triangle.

Correct  c = 29 m, a = 21 m  and b = 20 m

Step-by-step explanation:

Given:

a = b + 1  longer leg a

c = b + 9 hypotenuse c

To solve this problem, we will use Pythagoras' theorem

c² = a² + b²

(b + 9)² = (b + 1)² + b²  

b² + 18 b + 81 = b² + 2 b + 1 + b²

2 b² - b² + 2 b - 18 b + 1 - 81 = 0

b² - 16 b - 80 = 0  we will factorize this equation

⇒ b² - 20 b + 4 b - 80 = b (b - 20) + 4 ( b - 20) = (b - 20) · (b + 4) = 0

(b - 20) · (b + 4) = 0 ⇒ b = 20  or b = - 4  false

we accepted b = 20 m

c = b + 9 = 20 + 9 = 29 m

c = 29 m

a = b + 1 = 20 + 1 = 21 m

a = 21 m

God is with you!!!

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

idk

step-by-step explanation: