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Sagot :
Answer:
x = [tex]\sqrt{10}[/tex]
Step-by-step explanation:
The 2 right triangles and the outer right triangle are similar, then ratios of corresponding sides are equal, that is
[tex]\frac{x}{5}[/tex] = [tex]\frac{2}{x}[/tex] ( cross- multiply )
x² = 10 ( take the square root of both sides )
x = [tex]\sqrt{10}[/tex]
Answer:
√10
Step-by-step explanation:
taking the smallest triangle;
y as the hypotenuse, x as the adjacent side, 2 as the opposite side
then: y²=x²+2²
x²=y²-2²= y²-4
taking the other triangle;
z as the hypotenuse, x as the adjacent side, 5 as the opposite side
then: z²=x²+5²
x²=z²-5² = z²-25
take both equations,
x²= y²-4
x²= z²-25
y²-4= z²-25
y²= z²-25+4 = z²-21
taking the biggest triangle (whole triangle);
(5+2)= 7 as the hypotenuse, z as the adjacent side, y as the opposite side
then; 7²=z²+y²
z²+y²=7² =49
but y²= z²-21;
z²+y² =49
z²+ z²-21 =49
2z²-21=49
2z²=49+21= 70
z²= 70/2 = 35
take x²= z²-25
x²= 35-25 = 10
[tex]x = \sqrt{10} [/tex]
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