Mathematics, 22.06.2019 00:30 danibe98r

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?

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Answer from: pandaman632

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

Answer from: Quest

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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

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