In a 45-45-90 triangle , R is the right angle . If RS = 10 , what is PS?
A.10√2
B. 5
C.5√2
D. 5√3
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In a 45-45-90 triangle , R is the right angle . If RS = 10 , what is PS?
A.10√2
B. 5
C.5√2
D. 5√3
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nasa picture po yung sagot Sa gauthmath po nang galing yang answer na yan ito po yung link https://www.gauthmath.com/solution/11-In-a-45-45-90-triangle-R-is-the-right-angle-If-RS-10-what-is-PS-A-10-sqrt-2-B-1698433469008901
Answer:
A.10√2
Proof using Long-cut Method:
45-45-90 triangle is an Isosceles triangle.
so RS = RP = 10
and the Hypotenuse is your PS,
so solve for PS or hypotenuse let's use Pythagorean Theorem:
c² = a² + b²
PS² = 10² + 10²
PS² = 100 + 100
PS = √200
PS = √100*2
PS = 10√2 ==> Proven!
Proof using shortcut Method:
in 45-45-90 triangle,
ratio of the sides are:
x : x : x√2 = leg1 : leg2 : hypotenuse
so if x = RS = 10,
then PS = hypotenuse = x√2 = 10√2
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