Geometry

Geometry Level 2

There are two integers with a sum of 90.
These two integers, along with 30, form the lengths of a right angled triangle.

Find the value of these two numbers.

40,50 60,30 90,0 10,80 20,70

Pavan Kumar by Pavan Kumar , 26, India

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2 solutions

I used the 3 − 4 − 5 3-4-5 right triangle as my hint.

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Hello & peace be upon you,

since it is right angled triangle, given base = 30, let a = height, c = hypotenuse,

c + a = 90

c = 90 - a (1st),

by pythagoras theorem,

c^2 = a^2 + 30^2 (2nd),

substitute (1st) into (2nd),

(90-a)^2 = a^2 + 30^2,

8100 - 180a + a^2 = a^2 + 900

a = 40 , c = 50,

therefore, 40 & 50 are the two numbers....

thanks...

0 Helpful 0 Interesting 0 Brilliant 0 Confused

its not stated that the two integers are sides of a triangle...they could be anything even 56,34 is a option in which base is 30 with hypo. as 34

Rishabh Mishra - 6 years, 1 month ago

by principle of right angle triangle.... 3n,4n and 5n, the only possible is 30,40 and 50 if n = 10

Ramiel To-ong - 4 years ago

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