The perimeter of an isosceles right triangle is 16+ 16 sqrt(2). What is the hypotenuse?
A. 8
B. 16
C. 4 sqrt(2)
D. 8 sqrt(2)
E. 16 sqrt(2)
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Anurag@Gurome
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Let the sides of triangle be x, x, and sqrt2*x.Mjkourtis wrote:The perimeter of an isosceles right triangle is 16+ 16 sqrt(2). What is the hypotenuse?
A. 8
B. 16
C. 4 sqrt(2)
D. 8 sqrt(2)
E. 16 sqrt(2)
2x + sqrt2*x = 16+16*sqrt2.
x(2 + sqrt2) = 8*sqrt2(2 + sqrt2).
x = 8*sqrt2.
Hypotenuse is x* sqrt2 = 8*sqrt2*sqrt2 = 16
The correct answer is B.
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The sides of an isosceles right triangle are proportioned: s : s : s√2.The perimeter of a certain isosceles right triangle is 16 + 16√2. What is the length of the hypoteneuse?
a. 8
b. 16
c. 4√2
d. 8√2
e. 16√2
OA is b.
Could someone please explain this answer?
thanks
So if s=side and h=hypotenuse, then h = s√2 and s = h/√2.
We can plug in the answers, which represent the hypotenuse.
Answer choice C: h = 4√2
s = (4√2)/√2 = 4.
p = 4 + 4 + 4√2 = 8 + 4√2.
Eliminate C. The perimeter needs to be quite a bit larger.
Answer choice B: h = 16
s = 16/√2 = (16*√2)/(√2*√2) = (16√2)/2 = 8√2.
p = 8√2 + 8√2 + 16 = 16 + 16√2. Success!
The correct answer is B.
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Mr. Anurag... Could u once again plzz xplain the same question in a slightly different manner? Guru Ny ... Your method is good
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anuprajan5
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Hi,
The ratio of sides of a right isosceles triangle will be in √2:√2:1 form where the angles facing these will be in 45:45:90 form.
By that logic, the sides to me should be 16, 8√2 and 8√2.
Therefore the hypotenuse - the longest side is 16
Answer B
Regards
Anup
The ratio of sides of a right isosceles triangle will be in √2:√2:1 form where the angles facing these will be in 45:45:90 form.
By that logic, the sides to me should be 16, 8√2 and 8√2.
Therefore the hypotenuse - the longest side is 16
Answer B
Regards
Anup
