QuestionMr. Barton's garden has sides $16 \mathrm{ft}$ , $x \mathrm{ft}$ , $x \mathrm{ft}$ , and $20 \mathrm{ft}$ . If the perimeter is $60 \mathrm{ft}$ , find $x$ . Options: (A) $12 \mathrm{ft}$ (B) $15 \mathrm{ft}$ (C) $18 \mathrm{ft}$ (D) $24 \mathrm{ft}$ .

Studdy Solution

STEP 1

Assumptions1. The top side of the garden measures16 ft. The left and right sides each measure x ft3. The bottom side of the garden measures20 ft4. The total perimeter of the garden is60 ft

STEP 2

The perimeter of a rectangle is given by the formula $Perimeter =2(Length + Width)$ In this case, the length is $x$ and the width is the average of the top and bottom sides.

STEP 3

Substitute the given values into the formula $60 =2(x + \frac{16 +20}{2})$

STEP 4

implify the equation $60 =2(x +18)$

STEP 5

Divide both sides of the equation by2 to isolate the term with $x$ $30 = x +18$

STEP 6

Subtract18 from both sides of the equation to solve for $x$ $30 -18 = x$

STEP 7

Calculate the value of $x$ $x =12$ So, the length of one of the sides, $x$ , is12 ft. Therefore, the correct answer is(A) $12 \mathrm{ft}$

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QuestionMr. Barton's garden has sides $16 \mathrm{ft}$ , $x \mathrm{ft}$ , $x \mathrm{ft}$ , and $20 \mathrm{ft}$ . If the perimeter is $60 \mathrm{ft}$ , find $x$ . Options: (A) $12 \mathrm{ft}$ (B) $15 \mathrm{ft}$ (C) $18 \mathrm{ft}$ (D) $24 \mathrm{ft}$ .

Studdy Solution

STEP 1

Assumptions1. The top side of the garden measures16 ft. The left and right sides each measure x ft3. The bottom side of the garden measures20 ft4. The total perimeter of the garden is60 ft

STEP 2

The perimeter of a rectangle is given by the formula $Perimeter =2(Length + Width)$ In this case, the length is $x$ and the width is the average of the top and bottom sides.

STEP 3

Substitute the given values into the formula $60 =2(x + \frac{16 +20}{2})$

STEP 4

implify the equation $60 =2(x +18)$

STEP 5

Divide both sides of the equation by2 to isolate the term with $x$ $30 = x +18$

STEP 6

Subtract18 from both sides of the equation to solve for $x$ $30 -18 = x$

STEP 7

Calculate the value of $x$ $x =12$ So, the length of one of the sides, $x$ , is12 ft. Therefore, the correct answer is(A) $12 \mathrm{ft}$

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Studdy Solution

STEP 1

Assumptions1. The top side of the garden measures16 ft. The left and right sides each measure x ft3. The bottom side of the garden measures20 ft4. The total perimeter of the garden is60 ft

STEP 2

The perimeter of a rectangle is given by the formulaPerimeter=2(Length+Width)Perimeter =2(Length + Width)Perimeter=2(Length+Width)In this case, the length is xxx and the width is the average of the top and bottom sides.

STEP 3

Substitute the given values into the formula60=2(x+16+202)60 =2(x + \frac{16 +20}{2})60=2(x+216+20​)

STEP 4

implify the equation60=2(x+18)60 =2(x +18)60=2(x+18)

STEP 5

Divide both sides of the equation by2 to isolate the term with xxx30=x+1830 = x +1830=x+18

STEP 6

Subtract18 from both sides of the equation to solve for xxx30−18=x30 -18 = x30−18=x

STEP 7

Calculate the value of xxxx=12x =12x=12So, the length of one of the sides, xxx, is12 ft. Therefore, the correct answer is(A) 12ft12 \mathrm{ft}12ft

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The perimeter of a rectangle is given by the formula $Perimeter =2(Length + Width)$ In this case, the length is $x$ and the width is the average of the top and bottom sides.

Substitute the given values into the formula $60 =2(x + \frac{16 +20}{2})$

implify the equation $60 =2(x +18)$

Divide both sides of the equation by2 to isolate the term with $x$ $30 = x +18$

Subtract18 from both sides of the equation to solve for $x$ $30 -18 = x$

Calculate the value of $x$ $x =12$ So, the length of one of the sides, $x$ , is12 ft. Therefore, the correct answer is(A) $12 \mathrm{ft}$