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3 years ago

the length of a rectangle plus its width is 24 cm. the area is 143 square cm. what are the length and width of the rectangle?

Mathematics

2 answers:

pickupchik [31]3 years ago

6 0

Answer:

L=13, w=11

Step-by-step explanation:

Rus_ich [418]3 years ago

3 0

Answer:

The rectangle is 13cm by 11cm (or 11cm by 13cm)

Step-by-step explanation:

Length plus width = 25

L+W = 24

Area is 143

A = LW

143 = LW

We have two equations and two unknowns

L+W = 24 Solve for W by subtracting L from each side W = 24-L

143 = LW

Now substitute into the second equation

143 = L(24-L)

Distribute

143 = 24L - L^2

Multiply by -1

-143 = -24L +L^2

-143 = L^2 -24L

Completing the square

-24/2 = -12 -12^2 =144

Add 144 to each side

-143+144 = L^2 -24L+144

1 = (L-12)^2

Take the square root of each side

±sqrt(1) = sqrt( (L-12)^2)

±sqrt(1) = (L-12)

Add 12 to each side

12±sqrt(1) = (L-12)+12

12±1 = L

13=L or 11=L

Now we need to find W

W = 24 - L

W = 24-13 W = 24-11

W = 11 or W =13

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