Question

The length of rectangle B is 25% greater than the length of rectangle A. The width of rectangle B is 3/ 5 × the width of rectangle A. Find the fraction area of rectangle B /area of rectangle A Give your answer in its simplest form.

Answer 1

Answer:

the fraction area of rectangle B /area of rectangle A=3/4

Answer 2

Given,

Length of rectangle B is 25% greater than the length of rectangle A.

The width of rectangle B is $\[\frac{3}{5} \times \]$ the width of rectangle A.

Solution,

Consider the length and width of rectangle A is $\[{l_A},{b_A}\]$ and length and width of rectangle B is $\[{l_B},{b_B}\]$

$\[\begin{array}{l}{l_B} = 1.25 \times {l_A} - - - - \left( 1 \right)\\{b_B} = \frac{3}{5} \times {b_A} - - - - \left( 2 \right)\end{array}\]$

Area of rectangle = length $\[ \times \]$ width

Calculate the fraction area of rectangle B /area of rectangle A

$\[{\rm{ = }}\frac{{{\rm{area}}\,{\rm{of}}\,{\rm{rectangle}}\,{\rm{B}}}}{{{\rm{area}}\,{\rm{of}}\,{\rm{rectangle}}\,{\rm{A}}}}\]$

$\[{\rm{ = }}\frac{{{l_B} \times {b_B}}}{{{l_A} \times {b_A}}}\]$

$\[{\rm{ = }}\frac{{1.25 \times {l_A} \times \frac{3}{5} \times {b_A}}}{{{l_A} \times {b_A}}}\]$

$\[{\rm{ = }}1.25 \times \frac{3}{5}\]$

$\[{\rm{ = }}\frac{{3.75}}{5}\]$

$\[{\rm{ = }}\frac{{375}}{{500}}\]$

$\[{\rm{ = }}\frac{3}{4}\]$

Hence the fraction area of rectangle B to rectangle A is $\[\frac{3}{4}\]$