A group of art students are painting a mural on a wall. the rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planning the mural to be (x + 4) by (2x + 5). what is the area of the remaining wall after the mural has been painted?

Question

23-03-2018
Mathematics

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A group of art students are painting a mural on a wall. the rectangular wall has dimensions of (6x + 7) by (8x + 5) and they are planning the mural to be (x + 4) by (2x + 5). what is the area of the remaining wall after the mural has been painted?

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hannah334 hannah334 · Answer 1 · 2018-03-23T19:45:32+01:00

First: Find x

I used the larger rectangle first but you can do either one.

I added (8x+5) + (8x+5) + (6x+7) + (6x+7) =360

I made the sides equal to 360 because a square’s interior angles are equivalent to 360 degrees.

(8x+5) + (8x+5) + (6x+7) + (6x+7) =360

28x+24 = 360

28x = 336

X = 12

Next: Implement 12 in for x in every equation and follow the formula for a rectangle’s area.

A = b*h

BIG SQUARE:

(8(12)+5) + (8(12)+5) + (6(12)+7) + (6(12)+7)

=360

LITTLE SQUARE:

2((2(12)+5) + (6(12)+7)) = 90

Lastly: Subtract the little squares area from the biggest square

360 - 90 = 270