Answer:
[tex]\boxed{\boxed{\pink{\bf \leadsto Value \ of \ a \ is \ 5cm \ and \ b \ is \ 2cm .}}}[/tex]
Step-by-step explanation:
Given that the area of PQRS is 45 cm²
Area of PXYS = 10cm²
Now , from the figure we can see that ,
[tex]\bf\implies SY + YR = SR \\\\\bf\implies PX+XQ = PQ [/tex]
Also , we see that ,
[tex]\bf\implies ar(PSYX)= PS\times SY \\\\\bf\implies ar(XYRQ) = XY\times RQ [/tex]
And , we know that area of rectangle as ,
[tex]\large\boxed{\red{\bf Area_{rectangle}=lenght\times breadth }}[/tex]
Finding a :-
[tex]\implies\bf ar(XYRQ) = XY\times RQ \\\\\bf\implies ( 45cm^2-10cm^2) = 7cm\times a \\\\\bf\implies 7a = 35cm^2 \\\\\bf\implies a =\dfrac{35cm^2}{7cm}\\\\\bf\implies\boxed{\red{\bf a = 5cm}}[/tex]
Finding b :-
[tex]\implies\bf ar(PSYX)= PS\times SY \\\\\bf\implies 10cm^2 = b \times 5cm \\\\\bf\implies b =\dfrac{10cm^2}{5cm} \\\\\bf\implies\boxed{\red{\bf b = 2cm}}[/tex]
Hence the value of a is 5cm and b is 2cm .
