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

Answer:

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

Step-by-step explanation:

Let

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

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

we know that

$\frac{x}{y}=\frac{6}{4}$ ------> 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