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Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

QOTD#29 If the smallest angle of a triangle measures 45
[#permalink]
31 May 2017, 06:31

1

Expert Reply

Question Stats:

If the smallest angle of a triangle measures 45 degrees, which of the following could be the ratio of the three angles of the triangle?

Indicate the all the options possible

A. 2:3:3

B. 3:4:5

C. 3:5:7

D. 9:10:17

E. 9:11:13

F. 15:17:18

_________________

Indicate the all the options possible

A. 2:3:3

B. 3:4:5

C. 3:5:7

D. 9:10:17

E. 9:11:13

F. 15:17:18

Drill 2

Question: 9

Page: 342

Question: 9

Page: 342

_________________

Sandy

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Re: QOTD#29 If the smallest angle of a triangle measures 45
[#permalink]
14 Jun 2017, 23:22

1

1

Fixed!

Retired Moderator

Joined: **07 Jun 2014 **

Posts: **4805**

WE:**Business Development (Energy and Utilities)**

Re: QOTD#29 If the smallest angle of a triangle measures 45
[#permalink]
02 Jul 2017, 14:44

1

Expert Reply

Explanation

The first part of each ratio represents 45 degrees.

For choice(A), the multiplier will be 45 divided by 2, or 22.5. The ratio adds up to 8 (2 + 3 + 3), so check that 8 × 22.5 = 180. It does, so choice (A) works.

For choice (B), based on 3 representing 45 degrees, the multiplier is 15. The ratio adds up to 12, and 12 × 15 = 180, so this choice works as well.

Using this approach, choice (C) does not work: The multiplier is again 15, but 15 × 15 does not equal 180.

Choice (D) works, with a multiplier of 5: 5 × 36 = 180. When you test the remaining two choices, neither one produces the 180 degrees you need for the triangle, so eliminate them.

Hence options A, B and D are correct!

_________________

Sandy

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The first part of each ratio represents 45 degrees.

For choice(A), the multiplier will be 45 divided by 2, or 22.5. The ratio adds up to 8 (2 + 3 + 3), so check that 8 × 22.5 = 180. It does, so choice (A) works.

For choice (B), based on 3 representing 45 degrees, the multiplier is 15. The ratio adds up to 12, and 12 × 15 = 180, so this choice works as well.

Using this approach, choice (C) does not work: The multiplier is again 15, but 15 × 15 does not equal 180.

Choice (D) works, with a multiplier of 5: 5 × 36 = 180. When you test the remaining two choices, neither one produces the 180 degrees you need for the triangle, so eliminate them.

Hence options A, B and D are correct!

_________________

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QOTD#29 If the smallest angle of a triangle measures 45
[#permalink]
04 Mar 2021, 09:57

1

Solution:

This question took me around 5 mins to crack. For me, it's definitely not an easy one.

So, as we know the smallest angles is 45 and the sum of all angles of triangle=180.

Thus, the other 2 angles should have a sum of 180-45=135

Therefore, the \(\frac{ratio of the two sides}{ smallest side}=\frac{135}{45}=\frac{3}{1}

\)

From the above ratio, the sides of the triangles will also be in the same ratio.

For eg. consider option A: the smallest side has to be 2 and the sum of other two sides=6

Thus , the ratio will be\( \frac{6}{2}=\frac{3}{1}

\)

Similarly when we try for other options, Option B and D satisfies the condition

IMO A, B & D

Hope this helps

This question took me around 5 mins to crack. For me, it's definitely not an easy one.

So, as we know the smallest angles is 45 and the sum of all angles of triangle=180.

Thus, the other 2 angles should have a sum of 180-45=135

Therefore, the \(\frac{ratio of the two sides}{ smallest side}=\frac{135}{45}=\frac{3}{1}

\)

From the above ratio, the sides of the triangles will also be in the same ratio.

For eg. consider option A: the smallest side has to be 2 and the sum of other two sides=6

Thus , the ratio will be\( \frac{6}{2}=\frac{3}{1}

\)

Similarly when we try for other options, Option B and D satisfies the condition

IMO A, B & D

Hope this helps

Moderator

Joined: **16 Apr 2020 **

Status:**Founder & Quant Trainer**

Affiliations: **Prepster Education**

Posts: **1479**

Location: **India**

WE:**Education (Education)**

Re: QOTD#29 If the smallest angle of a triangle measures 45
[#permalink]
04 Mar 2021, 10:50

sandy wrote:

If the smallest angle of a triangle measures 45 degrees, which of the following could be the ratio of the three angles of the triangle?

Indicate the all the options possible

A. 2:3:3

B. 3:4:5

C. 3:5:7

D. 9:10:17

E. 9:11:13

F. 15:17:18

Indicate the all the options possible

A. 2:3:3

B. 3:4:5

C. 3:5:7

D. 9:10:17

E. 9:11:13

F. 15:17:18

A. \(2x + 3x + 3x = 180\)

\(x = \frac{180}{8} = 22.5\)

22.5 x 2 = 45

B. \(3x + 4x + 5x = 180\)

\(x = \frac{180}{12} = 15\)

15 x 3 = 45

C. \(3x + 5x + 7x = 180\)

\(x = \frac{180}{15} = 12\)

Cannot make 45

D. \(9x + 10x + 17x = 180\)

\(x = \frac{180}{36} = 5\)

9 x 5 = 45

E. \(9x + 11x + 13x = 180\)

\(x = \frac{180}{33} = 5.45\)

Cannot make 45

F. \(15x + 17x + 18x = 180\)

\(x = \frac{180}{8} = 3.6\)

Cannot make 45

Hence, A, B and D

_________________

I hope this helps!

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

gmatclubot

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