A company's logo consists of semicircles constructed on the sides of

Question

https://gmatclub.com/forum/download/file.php?id=58605 A company's logo consists of semicircles constructed on the sides of a right isosceles triangle. What is the total perimeter of the logo? A. 6\pi +\pi\sqrt{2} B. 6\pi +2\pi\sqrt{2} C. 6\pi +3\pi\sqrt{2} D. 6\pi +4\pi\sqrt{2} E. 6\pi +5\pi\sqrt{2} Project PS Butler Subscribe to get Daily Email - Click Here | Subscribe via RSS - RSS 2020-10-27_13-55-00.png

AjitJangale · Answer

Hi Bunnel,

I got answer 6π+3π \sqrt{2} . But did not match any of answer choices.

Could you please confirm answer choices.

rocky620 · Answer

Perimeter of smaller circles = 3π + 3π
Perimeter of bigger circle = 3 \sqrt{2} π

Total perimeter = 6π + 3 \sqrt{2} π

It can be option C (may be a typo of 1 in the option)

Bunuel · Answer

__________________________
Edited the typos. Thank you!

akadiyan · Answer

A company's logo consists of semicircles constructed on the sides of a right isosceles triangle. What is the total perimeter of the logo?

We know the side of smaller squares are the diagonal of the circle.

Diagonal of the smaller circles = 6
So circumference =  \pi d = 6 \pi

Circumference of semi circle = 3 \pi

Now coming to bigger circle

According to Pythagorean theorem , C =  \sqrt{A^2 + B^2} 
C =  \sqrt{6^2 + 6^2 } 
C = 72 
C = 6 \sqrt{ 2}

Now we have the length of third side which is equal to diagonal of the circle = 6 \sqrt{ 2}

Diagonal = 6 \sqrt{ 2} 
Circumference =  \pi d =  \pi 6 \sqrt{ 2} 
Circumference of semi circle =  \pi 3 \sqrt{ 2}

Perimeter = 3 \pi  + 3 \pi  + 3 \pi  \sqrt{ 2} 
6 \pi  + 3 \pi  \sqrt{ 2}

Ans:   C

mdsaddamforgmat · Answer

Correct option C
Isosceles side circle dia = 6
Therefore perimeter of half circle on the isosceles side = πd/2 = 3 π
Length of Hypotenuse = 6√2
Therefore perimeter of half circle on the hypotenuse side = πD/2 = π6√2/2 = 3√2π
Hence, total perimeter = 2x(3 π) + 3√2π = 6π+3π√2

GCMEMBER · Answer

A company's logo consists of semicircles constructed on the sides of a right isosceles triangle. What is the total perimeter of the logo?

Third side of the triangle = 6√2
Circumference of big circle = 3π√2

Circumference of each small circle = 3π

Total perimeter = 2*3π + 3π√2
= 6π + 3π√2

Choice C is the answer.

ScottTargetTestPrep · Answer

Solution:
 
We see that the perimeter of the company logo consists of the two equal and shorter semicircular arcs and one longer semicircular arc. Since the diameter of each of the smaller semicircles is 6, each of their semicircular arcs is ½ x 6 x π = 3π. Since the triangle in the middle is an isosceles right triangle (i.e., a 45-45-90 triangle), with a leg length of 6, its hypotenuse is 6√2. Since the hypotenuse of the triangle is also the diameter of the larger semicircle, its semicircular arc is ½ x 6√2 x π = 3π√2. Therefore, the perimeter of the logo is 3π + 3π + 3π√2 = 6π + 3π√2.

Answer: C

mattboutte · Answer

Good question about isosceles right triangles!

A company's logo consists of semicircles constructed on the sides of

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A company's logo consists of semicircles constructed on the sides of

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards