Question

Question 5 (ii)
Find the perimeters of the rectangle BCDE in this figure. Whose perimeter is greater?

Answer 1

$\text{In rectangle BCDE, BE}=\text{2}\frac{\text{3}}{\text{4}}\text{cm, ED}=\frac{\text{7}}{\text{6}}\text{cm}$
$\text{Perimeter of rectangle}=\text{2(length}+\text{breadth)}=2\left(2\frac{3}{4}+\frac{7}{6}\right)=2\left(\frac{11}{4}+\frac{7}{6}\right)=2\left(\frac{33+14}{12}\right)=\frac{47}{6}=7\frac{5}{6}\text{cm}\text{Thus, the perimeter of rectangle BCDE is 7}\frac{\text{5}}{\text{6}}\text{cm}$
$\text{Comparing the perimeter of triangle and that of rectangle}$
$\text{8}\frac{\text{17}}{\text{20}}\text{cm}>\text{7}\frac{\text{5}}{\text{6}}\text{cm}$
$\text{Therefore, the perimeter of triangle ABE is greater than rectangle BCDE}$.