perplexus.info :: Shapes : Triangle Area and Integer Finding

Triangle Area and Integer Finding (Posted on 2016-07-23)

Triangle EFG is a right angled triangle (right angled at ∠EGF) with EG = 7, FG = 24.
Point P is the midpoint of EF, and:
H is on the same side of line EF as G so that EH = FH = 15, and:
The area of triangle GHP is expressible as x*√y/z, where each of x, y and z is a positive integer, and:
x and z are relatively prime, and y is not divisible by the square of any prime.

Determine x, y and z

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Full solution

Comment 2 of 2 |

GP=FP=25/2

FH=15

since FPH is a right angle, by pythagorus,

PH^2=15^2-(25/2)^2

PH=5√(11)/2

angle EPG = 2arcsin(7/25)

angle GPH = 90-2arcsin(7/25)

we can now find the area sought with the SAS area formula:

Area(GHP)=(1/2)(25/2)(5√(11)/2)(sin(90-2arcsin(7/25))

=527√(11)/40

Posted by Jer on 2016-07-26 11:39:54

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