Source: Official Guide for the GMAT 13th Ed. Problem Solving; #104 Official Guide for the GMAT 2015 14th Ed. Problem Solving; #104

1

If a square mirror has a 20-inch

If a square mirror has a 20-inch diagonal, what is the approximate perimeter of the mirror, in inches?

3 Explanations

1

Nathaniel Gooden

It is simply two 3:4:5 triangles. If you divide the square into two triangles and make similar triangles then you can compare. The diagonal is 20 which is 5 x "4". Multiply "4" to the 3 and 4 on the 3:4:5 triangle to get 12:16:20. Now you have the sides of one half of the square. That being 12 and 16. Add them up:
12
12
16
16
=56, which is approximate to 60....Answer Choice B.

Dec 20, 2017 • Comment

1

Let´s start with one of the two 45 -45 - 90 triangles.

It follows a proportion of: x - x - x * (root of 2) (opposite sides of the angles).

Since 20 is the hypotenuse, 20 = x * (root of 2)

So, x = (20 / (root of 2) )

If the perimeter = 4x,

4x = 4 * (20 / (root of 2) ) = (80 / (root of 2) )

Multiply numerator and denominator by root of 2:

(80 * (root of 2)) / ((root of 2) * (root of 2))

(80 * (root of 2)) / 2

(40* (root of 2)) = 57 prox.

Correct answer = 60.

Jan 26, 2015 • Comment

2

Gravatar Mike McGarry, Magoosh Tutor

Dec 28, 2013 • Comment

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Section 5.3 Problem Solving

Section 5.3 Problem Solving

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