1.16: A Figure 1 shows the rectangle .

4PM1/1R/June/2023 — Question 1 · 4 marks

1.16 diagram 1
A
(a+b2)cm\displaystyle (a + b\sqrt{2})\mathrm{cm}
Figure 1 shows the rectangle ABCD\displaystyle ABCD.
AD=BC=(4−2)cmandAB=DC=(a+b2)cmwhereaandb are integers.AD = BC = (4 - \sqrt{2}) \mathrm{cm} \mathrm{and} AB = DC = (a + b\sqrt{2}) \mathrm{cm} \mathrm{where} a \mathrm{and} b \text{ are integers.}
The area of the rectangle is (10+2)cm2\displaystyle (10 + \sqrt{2}) \mathrm{cm}^2
Find the value of a\displaystyle a and the value of b\displaystyle b
Show your working clearly.
(4)