Priyaranjan wrote:Q. If a square mirror has a 20 inch diagonal, what is the appropriate perimeter of the mirror, in inches?
A) 40
B) 60
C) 80
D) 100
E) 120
Solution:
We are given that a square has a 20-inch diagonal, and we must find the perimeter of the square. We first need to determine the length of the side of the square. To determine the length of the side, we note that the diagonal of a square is also the hypotenuse of a 45-45-90 triangle, with length ratio of s : s : s√2, where s is the length of one of the sides. We thus can use this knowledge to see that: diagonal of a square = side√2 = s√2
20 = s√2
s = 20/√2
Notice that there is a square root in the denominator, which is an inappropriate form. The fraction must be re-expressed by the technique called "rationalizing the denominator." We can multiply 20/√2 by √2/√2. This gives us:
s = (20/√2) × (√2/√2)
s = (20√2)/√4
s = (20√2)/2
s = 10√2
We also should have memorized that the approximate value of √2 is 1.4. Thus, one side of the square is about 10 x 1.4 = 14 inches.
Finally, the perimeter of the square is about 4 x 14 = 56 inches. Since we are asked to approximate, the closest answer is 60.
Answer:
B
√2x.
√2x.
