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Verizon [17]
3 years ago
5

The area of a room is 396 square feet. The length is (x + 8) feet and the width is (x + 4) feet. Find the dimensions of the room

.
You only need to find the length and width.
Mathematics
2 answers:
Pepsi [2]3 years ago
5 0

Answer:

Area of rectangle (A) is given by:

A = lw

where, l is the length and w is the width of the rectangle.

As per the statement:

The area of a room is 396 square feet.

The length is (x + 8) feet and the width is (x + 4) feet.

⇒A = 396 square feet , l = (x+8) feet and w = (x+4) feet

Substitute these given values we have;

396 = (x+8)(x+4)

⇒396 = x^2+4x+8x+32

Combine like terms;

⇒396 = x^2+12x+32

Subtract 32 from both sides we have;

364 = x^2+12x

or

x^2+12x-364 =0

⇒x^2+26x-14x-364 = 0

⇒x(x+26)-14(x+26)=0

⇒(x+26)(x-14) = 0

By zero product property we have;

x+26 = 0 or x-14 = 0

⇒x = -26 and x = 14

Since, side cannot be in negative.

⇒x = 14

then;

l = x+8 = 14+8 = 22 feet

w = x+4 = 14+4 = 18 feet

Therefore, the dimensions of the room are:

l = 22 feet and w = 18 feet

alisha [4.7K]3 years ago
3 0
L:18ft
W:22ft
Hope it helps
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