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3 years ago

A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?

Mathematics

1 answer:

Nataliya [291]3 years ago

5 0

9514 1404 393

Answer:

3a by 4a

Step-by-step explanation:

For dimensions L and W, the area and perimeter are ...

A = LW = 12a^2

P = 2(L+W) = 14a

Using the second equation, we can find L:

L +W = 7a . . . . . divide by 2

L = 7a -W

Substituting into the area formula gives the quadratic ...

(7a -W)(W) = 12a^2

W^2 -7aW +12a^2 = 0 . . . . arrange in standard form

(W -3a)(W -4a) = 0 . . . . . . . factor (find factors of 12 that total 7)

Then we have the two solutions ...

W = 3a, L = 4a

W = 4a, L = 3a

The rectangle dimensions are 3a by 4a.

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3 years ago

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2 years ago

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3 years ago

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3 years ago

Find the values of x and y.

timurjin [86]

Answer:

x= 38

y= 71

Step-by-step explanation:

The triangle shown in the figure is an isosceles triangle, a triangle having two sides equal.

The two sides marked with a "dash" are said to be equal.

If we label off the triangle as ABC with AD being the extended length (containing 108°).

We'll get,

AB = AC

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*Property*

"If two sides of a triangle are equal their corresponding base angles are equal too."

=> ∠BAC = ∠BCA . . . . (¡)

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

From the figure, ∠BCA is equal to y.

*Property*

"Two angles on a straight line sum up to 180°"

∠BAC can be found out by subtracting 109° from the straight angle (180°).

=> ∠BAC = 180 - 109

=> ∠BAC = 71°

Substituting these values in eqn. (¡):

71 = y

Hence, the value of y is 71°

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

*Property*

"The exterior angle(angle on the extended side) of a triangle is equal to the sum of it's interior opposite angles."

Here,

Interior angles = x and y (= 71)
Exterior Angle = 109°

=> 109 = x + 71

=> 109 - 71 = x

=> x = 38°

Hence, the value of x is 38°.

4 0

2 years ago

A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?​

A Rectangular has area 12a^2 and perimeter 14a what are the dimensions of this Rectangular?