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3 years ago

Please help me with the work because i dont understand this.

Mathematics

1 answer:

Alexandra [31]3 years ago

7 0

Answer:

The dimension are 20 ft by 15 ft

Step-by-step explanation:

A = l*w

P = 2(l+w)

we know the area = 300

and the perimeter = 70

300 = lw

70 = 2 (l+w)

divide by 2

70/2 = 2/2 (l+w)

35 = l+w

subtract w

35-w = l+w-w

35 -w =l

substitute this into 300 = lw

300 = (35-w) * w

distribute

300 = 35w - w^2

subtract 300 from each side

0 = -w^2 +35w - 300

divide by -1

0 = w^2 - 35w + 300

factor

0= (w-15) (w-20)

using the zero product property

w-15 = 0 w-20 =0

so w=15, w=20

if w=15 then l=35 -w l = 35-15 l=20

if w=20 then l=35-w l= 35-20 = 15

The dimension are 20 ft by 15 ft

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E. Find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) Ć(1, -3).

AleksAgata [21]

Answer:

Length of sides of triangle are: AB = 15.13, BC = 12.72, AC = 9.21

Step-by-step explanation:

We need to find the length of sides of the triangle whose vertices are A (7,4), B (-8, 6) C(1, -3).

We have three sides of triangle AB, BC and AC

The length of side can be calculated using distance formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Now finding lengths of sides AB, BC and AC

i) Length of side AB

We have A (7,4), B (-8, 6)

and $x_1=7, y_1=4, x_2=-8, y_2=6$

Putting values in formula and finding length

$Length \ of \ side \ AB \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AB \ =\sqrt{(-8-7)^2+(6-4)^2}\\Length \ of \ side \ AB \ =\sqrt{(-15)^2+(2)^2}\\Length \ of \ side \ AB \ =\sqrt{225+4}\\Length \ of \ side \ AB \ =\sqrt{229}\\Length \ of \ side \ AB \ =15.13$

So, Length of side AB is 15.13

ii) Length of side BC

We have B (-8, 6) and C(1, -3)

and $x_1=-8, y_1=6, x_2=1, y_2=-3$

Putting values in formula and finding length

$Length \ of \ side \ BC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ BC \ =\sqrt{(1-(-8))^2+(-3-6)^2}\\Length \ of \ side \ BC \ =\sqrt{(1+8)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{(9)^2+(-9)^2}\\Length \ of \ side \ BC \ =\sqrt{81+81}\\Length \ of \ side \ BC \ =\sqrt{162}\\Length \ of \ side \ BC \ =12.72$

So, Length of side BC is 12.72

iii) Length of side AC

We have A (7,4)and C(1, -3)

and $x_1=7, y_1=4, x_2=1, y_2=-3$

Putting values in formula and finding length

$Length \ of \ side \ AC \ =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Length \ of \ side \ AC \ =\sqrt{(1-7)^2+(-3-4)^2}\\Length \ of \ side \ AC \ =\sqrt{(-6)^2+(-7)^2}\\Length \ of \ side \ AC \ =\sqrt{36+49}\\Length \ of \ side \ AC \ =\sqrt{85}\\Length \ of \ side \ AC \ =9.21$