Question

The perimeter of a rectangle is 16cm, and the area of the same rectangel is 8 cm^2. What is the diagonal length of that rectangle?

Answer 1

Answer:

4\sqrt{3}

Step-by-step explanation:

Perimeter= 2(l+b)

l*b=8cm

16=2(l+b)

l+b=8

Squaring on both sides

$l^{2}+2lb+b^{2}=64\\ l^{2} +b^{2} =64-2*8\\ l^{2} +b^{2}=64-16\\ l^{2} +b^{2}=48$

$diagonal^{2}=l^{2}+b^{2}\\ diagonal^{2}=48\\diagonal=\sqrt{48}\\diagonal =4\sqrt{3}$