Question

a carpenter is building a rectangular deck. the deck should have a width, $f(x)$, to length, $g(x)$, ratio of 2 to 3. the area of the deck is represented by the function $h(x)$. complete the table with the missing side lengths and areas of the deck.

$x$

$f(x)$

$g(x)$

$h(x)$

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1

2

3

$\boldsymbol{✓}$

2

4

$\boldsymbol{✓}$

24

5

$\boldsymbol{✓}$

15

150

10

20

30

$\boldsymbol{✓}$

Explanation:

Step1: Calculate h(1) (area)

Area = width × length, so $h(1) = f(1) \times g(1) = 2 \times 3 = 6$

Step2: Find g(2) via ratio

Width:length = 2:3, so $g(2) = f(2) \times \frac{3}{2} = 4 \times \frac{3}{2} = 6$

Step3: Find f(5) via ratio

Width:length = 2:3, so $f(5) = g(5) \times \frac{2}{3} = 15 \times \frac{2}{3} = 10$

Step4: Calculate h(10) (area)

Area = width × length, so $h(10) = f(10) \times g(10) = 20 \times 30 = 600$

Answer:

$x$	$f(x)$	$g(x)$	$h(x)$
2	4	6	24
5	10	15	150
10	20	30	600