Question

GEOMETRY! PLEASE SHOW YOUR WORK. (updated picture)

Answer 1

x = 144

Explanation:

Height Theorem

60² = 25·x

3600 = 25x

x = 3600 : 25

x = 144

Answer 2

Given:

The base of the given triangle has two part:

Left( left side of the hypotenuse) = 25

Right ( right side of the hypotenuse) = x

The altitude (h) = 60

To find the value of x.

Formula:

By Altitude rule we know that, the altitude of a triangle is mean proportional between the right and left part of the hypotenuse,

`(left)/(altitude) =(altitude)/(right)`

Now,

Putting,

left = 25, altitude = 60 and right = x we get,

`(25)/(60) =(60)/(x)`

or,
`(25)(x )=(60)(60)` [ by cross multiplication]

or,
`x = (3600)/(25)`

or,
`x = 144`

Hence,

The value of x is 144.