Question

The ratio of the corresponding sides of two similar triangles is 4:9. the length of the smaller rectangle is 16 cm and its width is 12 cm. what is the perimeter of the larger rectangle

Answer 1

The perimeter of the larger rectangle is 126 cm.

Explanation

The ratio of the corresponding sides of two similar rectangles is $4:9$

Given that, the length of the smaller rectangle is 16 cm and its width is 12 cm

Lets assume, the length and width of larger rectangle are $x$ and $y$ respectively.  

(Length of smaller / Length of larger) = 4 : 9

$\frac{16}{x}=\frac{4}{9}\\ \\ 4x = 16*9\\ \\ 4x= 144 \\ \\ x= \frac{144}{4}=36$

So, the length of larger rectangle is 36 cm.

 (Width of smaller / Width of larger) = 4 : 9

$\frac{12}{y}=\frac{4}{9}\\ \\ 4y= 12*9\\ \\ 4y= 108\\ \\ y= \frac{108}{4}=27$

So, the width of larger rectangle is 27 cm.

Thus, the perimeter of the larger rectangle $=2(length+width)= 2(36+27)= 2(63)=126 cm.$