Question

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Answer 1

h = 5

Explanation:

The value of h can be obtained by using area of triangle formula as well as distance formula.

`A(\triangle ABC) =(1)/(2) * AB* AC \\ \\ 60 = (1)/(2) * \sqrt{ {( - 3 + 3)}^(2) + (9 + 6) ^(2) } \\ * \sqrt{ {(h + 3)}^(2) + {(9 - 9)}^(2) } \\ \\ 60 * 2= \sqrt{ {( - 0)}^(2) + (15) ^(2) } \\ * \sqrt{ {(h + 3)}^(2) + {(0)}^(2) } \\ \\ 120= \sqrt{ 0 + (15) ^(2) } * \sqrt{ {(h + 3)}^(2) + 0 } \\ \\ 120= \sqrt{ (15) ^(2) } * \sqrt{ {(h + 3)}^(2) } \\ \\ 120 = 15(h + 3) \\ \\ (120)/(15) = h + 3 \\ \\ 8 = h + 3 \\ \\ h = 8 - 3 \\ \\ h = 5`

Answer 2

h = 5

Explanation:

area = 1/2 base × hight

base = 3 +h

hight =9 + 6 = 15

60 = 1/2 × 15 × (3+h)

120/15 = 3 + h

8 = 3 + h

h = 5