5. Find the perimeters of (i)\bigtriangleup\! ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?

         

Answers (1)

The perimeter of \bigtriangleup\! ABE^{} = AB + BE + AE 

                                        =\frac{5}{2}+2\frac{3}{4}+3\frac{3}{5}

                                        =\frac{5}{2}+\frac{4\times2+3}{4}+\frac{3\times5+3}{5}

                                        =\frac{5}{2}+\frac{11}{4}+\frac{18}{5}

Noe, The LCM of 2,4 and 5 is 20. So let's make the denominator of all fraction, 20.

So,

The perimeter of \bigtriangleup\! ABE^{} :

    =\frac{5}{2}\times\frac{10}{10}+\frac{11}{4}\times\frac{5}{5}+\frac{18}{5}\times\frac{4}{4}

   =\frac{50}{20}+\frac{55}{20}+\frac{72}{20}

    =\frac{50+55+72}{20}

    =\frac{177}{20}cm

 

Now,

The perimeter of rectangle BCDE = 2 x ( BE + ED )

=2\times\left (2\frac{3}{4}+\frac{7}{6} \right )

=2\times\left (\frac{4\times2+3}{4}+\frac{7}{6} \right )

=2\times\left (\frac{11}{4}+\frac{7}{6} \right )

The LCM of 4 and 6 is 12. So let's make the denominator of both fractions equal to 12.

=2\times\left (\frac{11}{4}\times\frac{3}{3}+\frac{7}{6}\times\frac{2}{2} \right )

=2\times\left (\frac{33}{12}+\frac{14}{12} \right )

=2\times\left (\frac{33+14}{12} \right )

=2\times\left (\frac{47}{12} \right )

=\frac{47}{6}cm

Hence The perimeter of the Triangle is 177/20 \:cm and the perimeter of Rectangle is  47/6 \: cm.

Now, we have 

\frac{177}{20} \:\: and\:\:\frac{47}{6}

LCM of 20 and 6 is 60, so let's make denominator of both fraction equal to 60.

So,

\frac{177}{20} =\frac{177}{20}\times\frac{3}{3}=\frac{531}{60}

And

\frac{47}{6}=\frac{47}{6}\times\frac{10}{10}=\frac{470}{60}

Now, Since 531 > 470 

\Rightarrow \frac{177}{20}>\frac{47}{6}.

\Rightarrow Area of Triangle > Area of Rectangle. 

Most Viewed Questions

Related Chapters

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
Buy Now
NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Buy Now
Boost your Preparation for JEE Main with our Foundation Course
 
Exams
Articles
Questions