How Cheenta works to ensure student success?
Explore the Back-Story

Sum of Sides of Triangle | PRMO-2018 | Problem No-17

Try this beautiful Problem on Sum of Sides of Triangle from Triangle from Prmo-2018, Problem 17.

Sum of Sides of Triangle - PRMO, 2018- Problem 17


Triangles $\mathrm{ABC}$ and $\mathrm{DEF}$ are such that $\angle \mathrm{A}=\angle \mathrm{D}, \mathrm{AB}=\mathrm{DE}=17, \mathrm{BC}=\mathrm{EF}=10$ and $\mathrm{AC}-\mathrm{DF}=12$
What is $\mathrm{AC}+$ DF ?

,

  • \(28\)
  • \(30\)
  • \(21\)
  • \(26\)
  • \(26\)

Key Concepts


Geometry

Triangle

Suggested Book | Source | Answer


Suggested Reading

Pre College Mathematics

Source of the problem

Prmo-2018, Problem-17

Check the answer here, but try the problem first

\(30\)

Try with Hints


First Hint

In \(\triangle ABC\) & \(\triangle DEF\), given that \(\angle A\)=\(\angle D\) & \(AB=DE\)=$17$ . $BC = EF = 10 $ and $AC – DF = 12.$ we have to find out $AC+DF$.

According to the question Let us assume that the point A coincides with D, B coincides with E. Now if we draw a circle with radius 10 and E(B) as center ....

Can you finish the problem?

Second Hint

Let M be the foot of perpendicular from B(E) to CF. So BM = 8. Hence $\mathrm{AM}=\sqrt{17^{2}-8^{2}}=\sqrt{(25)(9)}=15$

Third Hint

Hence $AF = 15 – 6 = 9$ & $AC = 15 + 6 = 21$

So $AC + DF = 30$

Subscribe to Cheenta at Youtube


Try this beautiful Problem on Sum of Sides of Triangle from Triangle from Prmo-2018, Problem 17.

Sum of Sides of Triangle - PRMO, 2018- Problem 17


Triangles $\mathrm{ABC}$ and $\mathrm{DEF}$ are such that $\angle \mathrm{A}=\angle \mathrm{D}, \mathrm{AB}=\mathrm{DE}=17, \mathrm{BC}=\mathrm{EF}=10$ and $\mathrm{AC}-\mathrm{DF}=12$
What is $\mathrm{AC}+$ DF ?

,

  • \(28\)
  • \(30\)
  • \(21\)
  • \(26\)
  • \(26\)

Key Concepts


Geometry

Triangle

Suggested Book | Source | Answer


Suggested Reading

Pre College Mathematics

Source of the problem

Prmo-2018, Problem-17

Check the answer here, but try the problem first

\(30\)

Try with Hints


First Hint

In \(\triangle ABC\) & \(\triangle DEF\), given that \(\angle A\)=\(\angle D\) & \(AB=DE\)=$17$ . $BC = EF = 10 $ and $AC – DF = 12.$ we have to find out $AC+DF$.

According to the question Let us assume that the point A coincides with D, B coincides with E. Now if we draw a circle with radius 10 and E(B) as center ....

Can you finish the problem?

Second Hint

Let M be the foot of perpendicular from B(E) to CF. So BM = 8. Hence $\mathrm{AM}=\sqrt{17^{2}-8^{2}}=\sqrt{(25)(9)}=15$

Third Hint

Hence $AF = 15 – 6 = 9$ & $AC = 15 + 6 = 21$

So $AC + DF = 30$

Subscribe to Cheenta at Youtube


Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

2 comments on “Sum of Sides of Triangle | PRMO-2018 | Problem No-17”

Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy
Cheenta

Cheenta Academy

Aditya Birla Education Academy

Aditya Birla Education Academy

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com
Menu
Trial
Whatsapp
Math Olympiad Program
magic-wandrockethighlight