In triangle FGH, FG=13cm, FH=13cm, GH=12cm. Find the area of triangle FGH.

In right-angled $\triangle FMG$, we have $FG^2 = FM^2 + GM^2$.

$$13^2 = 12^2 + GM^2$$ $$169 = 144 + GM^2$$ $$GM^2 = 169 - 144$$ $$GM^2 = 25$$ $$GM = \sqrt{25}$$ $$GM = 5 \text{ cm}$$

In right-angled $\triangle FMH$, we have $FH^2 = FM^2 + MH^2$.

$$15^2 = 12^2 + MH^2$$ $$225 = 144 + MH^2$$ $$MH^2 = 225 - 144$$ $$MH^2 = 81$$ $$MH = \sqrt{81}$$ $$MH = 9 \text{ cm}$$

The length of GH is the sum of GM and MH.

$$GH = GM + MH$$ $$GH = 5 \text{ cm} + 9 \text{ cm}$$ $$GH = 14 \text{ cm}$$

The length of GH is $\text{14 cm}$.