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3 years ago

12

CRITICAL THINKING The total area of the polygon is 176 square feet. What is the value of $x$ ?

1 answer:

Katarina [22]3 years ago

8 0

Answer:

x = 6

Step-by-step explanation:

this figure involves two triangle and one rectangle

for area of rectangle= Length * Width = 16 * 8 = 128 feet^2

for area of one triangle = 1/2 * base * height = 1/2 * x *8 = 4x

for two triangles = 8x ft^2 total

whole area = two triangles + one rectangle

176 = 8x + 128

8x =48

x = 6

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Please solve this for me using substitution

Vinvika [58]

<h2> <u>Explanation</u><u>:</u></h2>

$\bf \underline{★Given-} \\$

$\textsf{4x + 5y = 8};$

$\textsf{5x + 4y = 12}$

$\bf \underline{★To\: find-} \\$

$\textsf{the value of x and y in equation?}$

$\bf \underline{★Solution-} \\$

$\sf \leadsto 4x + 5y = 8 - - - (i)$

$\sf \leadsto 5x + 4y = 12 - - - (ii)$

By first equation,

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x = 8 - 5y$

$\sf \leadsto x = \dfrac{8 - 5y}{4}$

$\textsf{Now, we can find the original value of Y.}\\$

$\sf \leadsto 5x + 4y = 12$

$\sf \leadsto 5 \bigg( \dfrac{8 - 5y}{4} \bigg) + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y}{4} + 4y = 12$

$\sf \leadsto \dfrac{40 - 25y + 16y}{4} = 12$

$\sf \leadsto \dfrac{40 - 9y}{4} = 12$

$\sf \leadsto 40 - 9y = 12(4)$

$\sf \leadsto 40 - 9y = 48$

$\sf \leadsto -9y = 48 - 40$

$\sf \leadsto -9y = 8$

$\sf \leadsto y = \dfrac{ -8}{9}$

$\textsf{Now, we can find the original value of X.}\\$

$\sf \leadsto 4x + 5y = 8$

$\sf \leadsto 4x + 5 \bigg( \dfrac{ -8}{9} \bigg) = 8$

$\sf \leadsto 4x - \dfrac{40}{9} = 8$

$\sf \leadsto \dfrac{36x - 40}{9} = 8$

$\sf \leadsto 36x - 40 = 8(9)$

$\sf \leadsto 36x - 40 = 72$

$\sf \leadsto 36x = 72 + 40$

$\sf \leadsto 36x = 112$

$\sf \leadsto x = \dfrac{112}{36}$

$\underline{\textsf{Answer-}}\\$

Therefore, the values of x and y are -8/9 and 112/36 respectively.

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