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

Rectangle C is 14 cm longer than B

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+(1)/(5)x`

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

`x+(1)/(5)x+(1)/(3)(x+(1)/(5)x) =x+ (1)/(5)x+(1)/(3)x+(1)/(15)x=x+(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+(1)/(5)x +x+(9)/(15)x=133\\x+x+x+(1)/(5)x +(9)/(15)x=133\\3x+(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+(1)/(5)*35=42\ cm` and the length of rectangle C is
`35+(9)/(15)*35=56\ cm`

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