Question

❗❗100POINTS❗❗+BRAINLIEST FOR CORRECT ANSWERShow that 8x²-6x-275=0thanks. ​

Answer 1

$\\ \rm\hookrightarrow \dfrac{1}{2}(Sum\:of\: parallel\:sides)(Height)=133$

$\\ \rm\hookrightarrow \dfrac{1}{2}(x+5+3x-2)(2x-3)=133$

$\\ \rm\hookrightarrow 4x+3(2x-3)=266$

$\\ \rm\hookrightarrow 4x(2x-3)+3(2x-3)=266$

$\\ \rm\hookrightarrow 8x^2-12x+6x-9=266$

$\\ \rm\hookrightarrow 8x^2-6x=266+9$

$\\ \rm\hookrightarrow 8x^2-6x=275$

$\\ \rm\hookrightarrow 8x^2-6x-275=0$

Answer 2

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Here's the solution ~

Area of a Trapezoid is :

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times (sum \: of \: parallel \: sides) \times height = 133 \: c {m}^{2}$

so ~

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times ((x + 5) + (3x - 2)) \times (2x - 3) = 133 \:$

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times (x + 5+ 3x - 2) \times (2x - 3) = 133 \:$

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times (4x + 3) \times (2x - 3) = 133 \:$

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times(8 {x}^{2} - 12x + 6x - 9) = 133 \:$

$\qquad \sf \dashrightarrow \: \dfrac{1}{2} \times(8 {x}^{2} - 6x - 9) = 133 \:$

$\qquad \sf \dashrightarrow \: (8 {x}^{2} - 6x - 9) =( 133 \times 2)\:$

$\qquad \sf \dashrightarrow \: 8 {x}^{2} - 6x - 9 =266\:$

$\qquad \sf \dashrightarrow \: 8 {x}^{2} - 6x - 9 - 266 = 0$

$\qquad \sf \dashrightarrow \: 8 {x}^{2} - 6x - 275 = 0$

hence, we got the required equation ~