Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
3.5k views
in Trigonometry by (53.3k points)

A pentagon is formed by cutting a triangular corner from a rectangular piece of paper. The five sides of the pentagon have lengths 13, 19, 20, 25 and 31, not necessarily in that order. The area of the pentagon is

(A) 459 sq. units

(B) 600 sq. units 

(C) 680 sq. units 

(D) 745 sq. units

1 Answer

+1 vote
by (53.1k points)
selected by
 
Best answer

Correct option (D) 745 sq. units

See Fig.

Since r2 + s2 = e2, e = 31 or e = 19 is not possible. Therefore, e equal to 13, 20 or 25.

The possibilities for triplet {r, s, e} are {5, 12, 13}, {12, 16, 20}, {15, 20, 25}, {7, 24, 25}.

Since 16, 15 and 24 do not appear among any of pair wise differences of 13, 19, 20, 25, 31, we have  a = 19, b = 25, c = 31, d = 20, e = 13.

Hence required area = 745 sq. units.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...