(a) Find the area and perimeter of the rectangle in the figure
(b) What is the length of $A C$ ?

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Solution

(a) Perimetre of rectangle $= 2 (\sqrt{2} + \sqrt{8}) = 6 \sqrt{2} u n i t s$

And area of rectangle $= \sqrt{2} \times \sqrt{8} = 4 s q . u n i t s$

(b) Length $A C$ is the diagonal .

Using Pythagorous , we get

$A C^{2} = (\sqrt{2})^{2} + (\sqrt{8})^{2}$

$⟹ A C^{2} = 2 + 8$

$⟹ A C = \sqrt{1} 0$

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