**Given that the length of DB is 14 cm and the shaded region is 115 square cm, find the lenght of AC, correct to 2 decimal places.**

**Solution**

Area of Triangle = Half base x height.

Area of Triangle ABC --> (1/2)(AC)(DX + 14)

Area of Triangle ACD --> (1/2)(AC)(DX)

Area of shaded area

--> Area of Triangle ABC - Area of Triangle ACD = 115

(1/2)(AC)(DX + 14) - (1/2)(AC)(DX) = 115

(1/2)(AC)(DX) + (1/2)(AC)(14) - (1/2)(AC)(DX) = 115

(1/2)(AC)(14) = 115

7(AC) =115

AC = 115 divided by 7

= 16.428

~ 16.43 (nearest to 2 decimal places)

**Answer: 16.43 cm**

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