Question

Helena creates two similar rectangles using exactly 100 cm of string. The smaller rectangles width and length are 4 cm by 6 cm respectfully. What are the dimensions of the larger rectangle? Rounded to the nearest whole number.

Answer 1

The dimensions of the larger rectangle are
`24\ cm` of length by
`16\ cm` of width

Explanation:

Let

x-----> the length of the larger rectangle

y-----> the width of the larger rectangle

we know that

`(x)/(y)=(6)/(4)` ------> by similar rectangles

`x=1.5y` -----> equation A

Find the perimeter of the smaller rectangle

`P=2(6+4)=20\ cm`

Find the perimeter of the larger rectangle

Subtract the perimeter of the smaller rectangle from 100 cm of string

`P=100-20=80\ cm`

Remember that

`80=2x+2y` ------>
`40=x+y` ------> equation B

substitute equation A in equation B

`40=1.5y+y`

`2.5y=40`

`y=16\ cm`

Find the value of x

`x=1.5(16)=24\ cm`

The dimensions of the larger rectangle are
`24\ cm` of length by
`16\ cm` of width