Question

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Answer 1

Answer:

h = 5

Step-by-step explanation:

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

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

Answer 2

Answer:

h = 5

Step-by-step 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