Question

PLEAZZZZZZZZZZ HELP ASAP

Answer 1

QUESTION 1

GIVEN:

$long \: base = 3 \times (short \: base)$

$height = (short \: base) - 2$

$area = 30 {in}^{2}$

IMPORTANT EQUATIONS

$trapezoid \: area = \frac{sum \: of \: bases}{2} \times height$

SOLVE:

$30 = \frac{short + long}{2} (short - 2)$
$30 = \frac{(short + 3short)}{2} \times (short - 2)$

$30 = \frac{4short}{2} (short - 2)$

$30 = 2{(short)}^{2} - 4(short)$

${short}^{2} - 2(short) - 15 = 0$

factor:

$(short - 5)(short + 3) = 0$

$short = 3 \: and \: - 5$
Negative five is not a reasonable answer, so we focus on the positive three and say that is the length of the short base.

so, the answers:

$short \: base = 3 \: in$

$long \: base = 3 \times 3 = 9 \: in$

$height = 3 - 2 = 1 \: in$

QUESTION 2

GIVEN
convert 3ft to inches.

$l = 32 + w$

$area = lw = 130 {in}^{2}$
or

$w = \frac{130}{l}$

substitute

$l = 32 + \frac{130}{l}$

solve for l:

${l}^{2} - 32 l- 130 = 0$
QUESTION 3

$x(x + 2) = 80$

solve for X

${x}^{2} + 2x - 80 = 0$
$(x - 10)(x + 8) = 0$

$x = 10 \: and \: - 8$

take the positive value since it's the only one that makes sense in this context.

so the two values are:

$10 \: and \: 8$