Respuesta :
Length and width of rectangle is 15 inches and 6 inches respectively
Solution:
Given that area of a rectangle is 90 square inch
Ratio of length to the width = 5: 2.
Need to determine length and width of rectangle.
As ratio of length to the width is 5 : 2
Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.
The formula for area of rectangle is given as:
[tex]\text { Area of rectangle }=\text { length of rectangle } \times \text { width of rectangle}[/tex]
Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:
[tex]\begin{array}{l}{90=5 x \times 2 x} \\\\ {=>90=10 x^{2}}\end{array}[/tex]
On solving the above expression for x we get
[tex]\begin{array}{l}{=>\frac{90}{10}=x^{2}} \\\\ {=>x^{2}=9} \\\\ {=>x=\sqrt{9}=3}\end{array}[/tex]
[tex]\begin{array}{l}{\text { Length of rectangle }=5 \times x=5 \times 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 \times} x=2 \times} 3=6 \text { inches }}\end{array}[/tex]
Hence length and width of rectangle is 15 inches and 6 inches.
