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# math

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A blackboard has an area of 28  and a perimeter of 22 ft. What are the dimensions of the board?

Feb 8, 2018

#2
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2[L + W] =22

L*W = 28

W = 28/L sub this in the first equation

Solve for L:

2 (L + 28/L) = 22

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

L + 28/L = 11

Write the left hand side as a single fraction.

Bring L + 28/L together using the common denominator L:

(L^2 + 28)/L = 11

Multiply both sides by a polynomial to clear fractions.

Multiply both sides by L:

L^2 + 28 = 11 L

Move everything to the left hand side.

Subtract 11 L from both sides:

L^2 - 11 L + 28 = 0

Factor the left hand side.

The left hand side factors into a product with two terms:

(L - 7) (L - 4) = 0

Find the roots of each term in the product separately.

Split into two equations:

L - 7 = 0 or L - 4 = 0

Look at the first equation: Solve for L.

L = 7 or L - 4 = 0

Look at the second equation: Solve for L.

L = 7       or L = 4         and        W=4      or W = 7

Feb 9, 2018

#1
0

Perimeter =2[L + W]
Area =L*W

2[L + W] =22
L*W = 28, solve for L, W
L =7 and W = 4, or
W = 4 and L =7

Feb 8, 2018
#2
+1

2[L + W] =22

L*W = 28

W = 28/L sub this in the first equation

Solve for L:

2 (L + 28/L) = 22

Divide both sides by a constant to simplify the equation.

Divide both sides by 2:

L + 28/L = 11

Write the left hand side as a single fraction.

Bring L + 28/L together using the common denominator L:

(L^2 + 28)/L = 11

Multiply both sides by a polynomial to clear fractions.

Multiply both sides by L:

L^2 + 28 = 11 L

Move everything to the left hand side.

Subtract 11 L from both sides:

L^2 - 11 L + 28 = 0

Factor the left hand side.

The left hand side factors into a product with two terms:

(L - 7) (L - 4) = 0

Find the roots of each term in the product separately.

Split into two equations:

L - 7 = 0 or L - 4 = 0

Look at the first equation: Solve for L.

L = 7 or L - 4 = 0

Look at the second equation: Solve for L.