Question

Here is rectangle A. Block A. Rectangle B is ¹/₅ longer than A Block B. Rectangle C is ¹/₃ longer than B Block C. The total length of all three rectangles is 133 cm. How much longer is rectangle C than B?

Answer 1

Answer:

Rectangle C is 14 cm longer than B

Step-by-step explanation:

Let  x be the length of Rectangle A. Rectangle B is ¹/₅ longer than A Block B,

Therefore the length of rectangle B is:

$x+\frac{1}{5}x$

Rectangle C is ¹/₃ longer than B, therefore the length of rectangle c is:

$x+\frac{1}{5}x+\frac{1}{3}(x+\frac{1}{5}x) =x+ \frac{1}{5}x+\frac{1}{3}x+\frac{1}{15}x=x+\frac{9}{15}x$

The total length of all three rectangles is 133 cm.

Length of rectangle A + Length of rectangle B + Length of rectangle C = 133 cm

$x+x+\frac{1}{5}x +x+\frac{9}{15}x=133\\x+x+x+\frac{1}{5}x +\frac{9}{15}x=133\\3x+\frac{12}{15}x=133\\ 45x+12x=1995\\57x=1995\\x=35cm$

Therefore the length of rectangle A is 35 cm, the length of rectangle B is $35+\frac{1}{5}*35=42\ cm$ and the length of rectangle C is $35+\frac{9}{15}*35=56\ cm$

Rectangle C is ¹/₃ longer than B, which is 14 cm (42\3) longer than B