Question

A lot is in the shape of a right triangle. The shorter leg measures 150m. The hypotenuse is 50m longer than the length of the longer leg. How long (in meters ) is the longer leg?

Answer 1

longer leg = 200 m

Explanation:

using Pythagoras' identity in the right triangle.

a² + b² = c² ( c is the hypotenuse and a, b the legs )

let x be the longer leg , then the hypotenuse is x + 50,

with shorter leg = 150 m

substitute these values into the equation

x² + 150² = (x + 50)² ← expand using FOIL

x² + 22500 = x² + 100x + 2500 ( subtract x² from both sides )

x² - x² + 22500 = x² - x² + 100x + 2500 ( simplify )

22500 = 100x + 2500 ( subtract 2500 from both sides )

22500 - 2500 = 100x + 2500 - 2500

20000 = 100x ( divide both sides by 100 )

`(20000)/(100)` =
`(100)/(100)` x , that is

200 = x

the longer leg is 200 m