MATH SOLVE

4 months ago

Q:
# The shorter leg of a right triangle is 7m shorter than the longer leg. the hypotenuse is 7m longer than the longer leg. find the side lengths of the triangle.

Accepted Solution

A:

--------------------------------------------

Define x :

--------------------------------------------

Let the shorter leg = x

Longer leg = x + 7

Hypotenuse = x + 7 + 7 = x + 14

--------------------------------------------

Solve x :

--------------------------------------------

a² + b² = c²

x² + (x+7)² = (x+14)²

x² + x² + 14x + 49 = x² + 28x + 196

2x² + 14x + 49 = x² + 28x + 196

x² - 14x - 147 = 0

(x - 21)(x + 7) = 0

x = 21 or x = - 7 (rejected, because length cannot be negative)

--------------------------------------------

Find the legs and hypotenuse:

--------------------------------------------

shorter leg = x = 21

longer leg = x + 7 = 21 + 7 = 28

hypotenuse = x + 14 = 21 + 14 = 35

----------------------------------------------------------------------------------------

Answer: The side length of the triangles are 21m, 28, and 35m.

----------------------------------------------------------------------------------------

Define x :

--------------------------------------------

Let the shorter leg = x

Longer leg = x + 7

Hypotenuse = x + 7 + 7 = x + 14

--------------------------------------------

Solve x :

--------------------------------------------

a² + b² = c²

x² + (x+7)² = (x+14)²

x² + x² + 14x + 49 = x² + 28x + 196

2x² + 14x + 49 = x² + 28x + 196

x² - 14x - 147 = 0

(x - 21)(x + 7) = 0

x = 21 or x = - 7 (rejected, because length cannot be negative)

--------------------------------------------

Find the legs and hypotenuse:

--------------------------------------------

shorter leg = x = 21

longer leg = x + 7 = 21 + 7 = 28

hypotenuse = x + 14 = 21 + 14 = 35

----------------------------------------------------------------------------------------

Answer: The side length of the triangles are 21m, 28, and 35m.

----------------------------------------------------------------------------------------