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The diagram gives information about two paintings, P and Q.
Each painting is in the shape of a rectangle.



Painting P has an area 1400 cm more than the area of painting Q.

Work out the area of painting P.

The diagram gives information about two paintings P and Q Each painting is in the shape of a rectangle Painting P has an area 1400 cm more than the area of pain class=

Respuesta :

Answer: 2600 cm^2

Step-by-step explanation:

FORMULA

Painting P area = Painting Q area +   1400

      so...

 40(3x-10)           =       30(x+15)        +   1400

 EXPAND                     EXPAND

 

 120x - 400          =       30x + 450     +   1400

                                                        SIMPLIFY

 120x-400            =        30x + 1850

         +400                             +400

 120x                    =         30x + 2250

 - 30x                             - 30x

   90x                   =                   2250      

DIVIDE BY 90              DIVIDE BY 90

     x                      =                   25

SO... Now we have to find the AREA of PAINTING P

LENGTH: (3x - 10)=  3(25) - 10 = 65cm

HEIGHT:  40cm

AREA OF PAINTING P = 65cm X 40cm = 2600cm^2

facundo3141592

By solving a system of equations, we will see that the area of painting P is 2,600 cm^2

How to get the area of painting P?

Remember that the area of a rectangle of length L and width W is:

A = L*W

Then the area of painting P is:

A = 40cm*(3x - 10)cm

The area of paint Q is:

A' = (30 cm)*(x + 15)cm

And que know that:

A = A' + 1400cm^2

Then we havea system of equations:

A = A' + 1400cm^2

A = 40cm*(3x - 10)cm

A' = (30 cm)*(x + 15)cm

First, we can replace the third equation into the first one to get:

A = (30 cm)*(x + 15)cm + 1400cm^2

And that must be equal to:

A = 40cm*(3x - 10)cm

So now we can solve:

40cm*(3x - 10)cm =  (30 cm)*(x + 15)cm + 1400cm^2

for x.

It gives:

120cm*x - 400cm^2 = 30cm*x + 1850 cm^2

120cm*x - 30cm*x = 1850cm^2 + 400cm2

x = (2250cm^2)/(90cm) = 25cm

Now that we know x, we can get the area of painting P.

A = 40cm*(3*25cm - 10cm) = 2,600cm^2

If you want to learn more about systems of equations, you can read:

https://brainly.com/question/13729904

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