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Q.104, PS GMAT Review 13th Edition

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by Brent@GMATPrepNow » Fri Apr 10, 2015 8:07 pm
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
Let x = the length of one side of the square
The diagonal creates a right triangle with each leg having length x and the hypotenuse with length 20.
Plug these values into the Pythagorean Theorem to get: x² + x² = 20²
Simplify: 2x² = 400
Divide both sides by 2 to get x² = 200
So, x = √200
Rewrite as x = 10√2

NOTE: For the GMAT, you should memorize approximations for √2, √3 and √5
√2 ≈ 1.4
So, 10√2 ≈ (10)1.4 ≈ 14

If each side of the square has length 14, then the perimeter of the square = (4)(14) = 56

The best approximation is [spoiler]B (60)[/spoiler]

Cheers,
Brent
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by Priyaranjan » Sun Apr 12, 2015 12:41 am
Sir,

I've got the same result, but followed another rule of the Triangles.

As this was a 90-45-45 degree triangle, the ratio of their sides would be x:x:√2x.
As √2x=20,x=20/√2.
Perimeter= 20*4/√2=80/√2≈57.1... (where √2=1.4)
So, the approximate value would be option B)60.

Kindly let me know about the process.

Thanking you
Brent@GMATPrepNow wrote:
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
Let x = the length of one side of the square
The diagonal creates a right triangle with each leg having length x and the hypotenuse with length 20.
Plug these values into the Pythagorean Theorem to get: x² + x² = 20²
Simplify: 2x² = 400
Divide both sides by 2 to get x² = 200
So, x = √200
Rewrite as x = 10√2

NOTE: For the GMAT, you should memorize approximations for √2, √3 and √5
√2 ≈ 1.4
So, 10√2 ≈ (10)1.4 ≈ 14

If each side of the square has length 14, then the perimeter of the square = (4)(14) = 56

The best approximation is [spoiler]B (60)[/spoiler]

Cheers,
Brent
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by GMATGuruNY » Sun Apr 12, 2015 2:26 am
If a square mirror has a 20-inch diagonal what is the closest approximate perimeter of the mirror, in inches?
A- 40
B- 60
C- 80
D- 100
E- 120
The diagonal of a square with side s = s√2.
Every test-taker should know that √2 ≈ 1.4.

We can PLUG IN THE ANSWERS, which represent the perimeter of the mirror.
When the correct answer is plugged in, the diagonal ≈ 20.

Answer choice D: 100
Since p=100, s=25.
Too big:
The side of the square cannot be longer than the diagonal.
Since the correct answer must be smaller, eliminate D and E.

Answer choice B: 60
Since p=60, s=15.
Diagonal = 15√2 ≈ (15)(1.4) = 21.
Success!

The correct answer is B.
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by Brent@GMATPrepNow » Sun Apr 12, 2015 6:21 am
Priyaranjan wrote:Sir,

I've got the same result, but followed another rule of the Triangles.

As this was a 90-45-45 degree triangle, the ratio of their sides would be x:x:√2x.
As √2x=20,x=20/√2.
Perimeter= 20*4/√2=80/√2≈57.1... (where √2=1.4)
So, the approximate value would be option B)60.

Kindly let me know about the process.

Thanking you
Hi Priyaranjan,

Your solution is perfect. It's quite similar to mine, except you used the rule about the ratios of a 45-45-90 triangle, and I used the Pythagorean Theorem to (essentially) duplicate that ratio.

Cheers,
Brent
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by Scott@TargetTestPrep » Fri Jun 26, 2015 8:43 am
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
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