HELP!!! find the value of x

Question

asked Oct 11, 2022 16.8k views

2 Answers

Mrig · Answer 1 · 2022-10-13T16:31:54+0000

Answer:

x = 12

Explanation:

Consider three orthogonal triangles (see picture)

1. The smallest triangle

2. The medium triangle

3. The big triangle that holds both triangles.

All are orthogonal (or right triangles) so you can use Pythagoras Theorem:

"The area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides"

Use Pythagoras theorem on triangle 1.

a^(2) = 3^(2) + 6^(2) = 45

Now user Pythagoras on triangle 2.

b^(2) = x^(2) + 6^(2) = x^(2) + 36

Now use Pythagoras on triangle 3 (the big triangle).

$(3 + x )^(2) = a^(2) + b^(2)\\x^(2) + 6x + 9 = a^(2) + b^(2)$

Now replace the values for
a^(2) and
b^(2) from the two equations derived from triangle 1 and 2:

x^(2) + 6x + 9 = 45 + x^(2) + 36

The two
x^(2) get cancelled out, so:

$6x + 9 = 45 + 36\\x = 12$

TA DA!