The length of a rectangular mural is 2ft. more than three times the width the area is 165 sq. ft. Find the Width And Length

We know that the formula for the area of a rectangle is:

$$A=lw$$

We know that the area is 165. Now we need to solve for the dimensions.

Let the width of the rectangle be "$$x$$"

Then the length of the rectangle is $$3x+2$$

Substitute.

$$(3x+2)(x)=156$$

Multiply the terms.

$$3x^2+2x=156$$

Bring the 156 over.

$$3x^2+2x-156=0$$

We have to use the quadratic formula to solve this now. Let us restate it:

$$x= \frac{-b± \sqrt{b^2-4ac} }{2a}$$

Now I’m going to fast forward this because all the rest is boring stuff and substitution. The answer is:

$$\frac{ \sqrt{469}-1 }{3}$$

Since we cannot have a negative answer, we must cancel out the other answer, which I did not include.

L×b=area
l=2+3b
2+3b ×b=165
3b²=163
b²=54.3
b=√54.3
b=7.37 or 7.4=7
b=7ft
l=2+3(7.4)
l=2+ 22.2
l=24.2=24
l=24ft

RELATED: