Math / Geometry

QuestionFill in the blank. A rectangular field has a width of $(a+b)^{3}$ meters and $a$ length of $2 a^{2}$ meters. Determine the area of this field for $a=5$ and $b=-3$ .
The area of the field is square meters.

Studdy Solution

STEP 1

1. The field is rectangular.
2. The width of the field is given by the expression $(a+b)^{3}$ .
3. The length of the field is given by the expression $2a^{2}$ .
4. Values for $a$ and $b$ are provided: $a=5$ and $b=-3$ .

STEP 2

1. Calculate the width of the field using the given expression and values for $a$ and $b$ .
2. Calculate the length of the field using the given expression and value for $a$ .
3. Determine the area of the field by multiplying the width and length.
4. Provide the final answer.

STEP 3

Calculate the width of the field:
$\text{Width} = (a+b)^{3}$
Substitute $a = 5$ and $b = -3$ :
$\text{Width} = (5 + (-3))^{3} = (5 - 3)^{3} = 2^{3} = 8 \text{ meters}$

STEP 4

Calculate the length of the field:
$\text{Length} = 2a^{2}$
Substitute $a = 5$ :
$\text{Length} = 2(5)^{2} = 2 \times 25 = 50 \text{ meters}$

STEP 5

Determine the area of the field by multiplying the width and length:
$\text{Area} = \text{Width} \times \text{Length}$ $= 8 \text{ meters} \times 50 \text{ meters}$ $= 400 \text{ square meters}$
The area of the field is:
$\boxed{400 \text{ square meters}}$

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QuestionFill in the blank. A rectangular field has a width of $(a+b)^{3}$ meters and $a$ length of $2 a^{2}$ meters. Determine the area of this field for $a=5$ and $b=-3$ .
The area of the field is square meters.

Studdy Solution

STEP 1

1. The field is rectangular.
2. The width of the field is given by the expression $(a+b)^{3}$ .
3. The length of the field is given by the expression $2a^{2}$ .
4. Values for $a$ and $b$ are provided: $a=5$ and $b=-3$ .

STEP 2

1. Calculate the width of the field using the given expression and values for $a$ and $b$ .
2. Calculate the length of the field using the given expression and value for $a$ .
3. Determine the area of the field by multiplying the width and length.
4. Provide the final answer.

STEP 3

Calculate the width of the field:
$\text{Width} = (a+b)^{3}$
Substitute $a = 5$ and $b = -3$ :
$\text{Width} = (5 + (-3))^{3} = (5 - 3)^{3} = 2^{3} = 8 \text{ meters}$

STEP 4

Calculate the length of the field:
$\text{Length} = 2a^{2}$
Substitute $a = 5$ :
$\text{Length} = 2(5)^{2} = 2 \times 25 = 50 \text{ meters}$

STEP 5

Determine the area of the field by multiplying the width and length:
$\text{Area} = \text{Width} \times \text{Length}$ $= 8 \text{ meters} \times 50 \text{ meters}$ $= 400 \text{ square meters}$
The area of the field is:
$\boxed{400 \text{ square meters}}$

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QuestionFill in the blank. A rectangular field has a width of (a+b)3(a+b)^{3}(a+b)3 meters and aaa length of 2a22 a^{2}2a2 meters. Determine the area of this field for a=5a=5a=5 and b=−3b=-3b=−3.The area of the field is square meters.

Studdy Solution

STEP 1

1. The field is rectangular.2. The width of the field is given by the expression (a+b)3(a+b)^{3}(a+b)3.3. The length of the field is given by the expression 2a22a^{2}2a2.4. Values for aaa and bbb are provided: a=5a=5a=5 and b=−3b=-3b=−3.

STEP 2

1. Calculate the width of the field using the given expression and values for aaa and bbb.2. Calculate the length of the field using the given expression and value for aaa.3. Determine the area of the field by multiplying the width and length.4. Provide the final answer.

STEP 3

Calculate the width of the field:Width=(a+b)3 \text{Width} = (a+b)^{3} Width=(a+b)3Substitute a=5a = 5a=5 and b=−3b = -3b=−3:Width=(5+(−3))3=(5−3)3=23=8 meters \text{Width} = (5 + (-3))^{3} = (5 - 3)^{3} = 2^{3} = 8 \text{ meters} Width=(5+(−3))3=(5−3)3=23=8 meters

STEP 4

Calculate the length of the field:Length=2a2 \text{Length} = 2a^{2} Length=2a2Substitute a=5a = 5a=5:Length=2(5)2=2×25=50 meters \text{Length} = 2(5)^{2} = 2 \times 25 = 50 \text{ meters} Length=2(5)2=2×25=50 meters

STEP 5

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QuestionFill in the blank. A rectangular field has a width of $(a+b)^{3}$ meters and $a$ length of $2 a^{2}$ meters. Determine the area of this field for $a=5$ and $b=-3$ .
The area of the field is square meters.

1. The field is rectangular.
2. The width of the field is given by the expression $(a+b)^{3}$ .
3. The length of the field is given by the expression $2a^{2}$ .
4. Values for $a$ and $b$ are provided: $a=5$ and $b=-3$ .

1. Calculate the width of the field using the given expression and values for $a$ and $b$ .
2. Calculate the length of the field using the given expression and value for $a$ .
3. Determine the area of the field by multiplying the width and length.
4. Provide the final answer.

Calculate the width of the field:
$\text{Width} = (a+b)^{3}$
Substitute $a = 5$ and $b = -3$ :
$\text{Width} = (5 + (-3))^{3} = (5 - 3)^{3} = 2^{3} = 8 \text{ meters}$

Calculate the length of the field:
$\text{Length} = 2a^{2}$
Substitute $a = 5$ :
$\text{Length} = 2(5)^{2} = 2 \times 25 = 50 \text{ meters}$