For the rectangle, the length of rectangle a is 7 cm and the width of the rectangle b is 3 cm.
What is the area of the rectangle?
The area of the rectangle is a product of the length and width of the rectangle.
Given
In the diagram shown, PQRS is a rectangle XY is parallel to PS, RY= 9cm.
Area of PQRS = 84cm^2
Area of PXYS = 21cm^2
The following formula is used to calculate the area of the rectangle;
[tex]\rm Area \ of \ rectangle =Length \times Width[/tex]
The length of the rectangle PQRS is a and width is ( 9+b).
Then,
[tex]\rm Area \ of \ rectangle =Length \times Width\\\\\rm Area \ of \ PQRS=a\times (9+b)\\\\84=9a+ab[/tex]
The length of the rectangle PXYS is a and the width is b.
Then,
[tex]\rm Area \ of \ rectangle =Length \times Width\\\\\rm Area \ of \ PQRS=a\times b\\\\ 21=ab[/tex]
Substitute the value of ab in equation 1
[tex]\rm 84=9a+ab\\\\ 84=9a+21\\\\9a=84-21\\\\9a=63\\\\a=\dfrac{63}{9}\\\\a=7[/tex]
Substitute the value of a, in equation 2
[tex]\rm ab=21\\\\7b=21\\\\b = \dfrac{21}{7}\\\\b=3[/tex]
Hence, the value of a is 7, and b is 3.
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