The length of a rectangular mural is 2 ft 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 3 x + 2
Substitute.
( 3 x + 2 ) ( x ) = 156
Multiply the terms.
3 x 2 + 2 x = 156
Bring the 156 over.
3 x 2 + 2 x − 156 = 0
We have to use the quadratic formula to solve this now. Let us restate it:
x = 2 a − b ± b 2 − 4 a c ​ ​
Now I'm going to fast forward this because all the rest is boring stuff and substitution. The answer is:
3 469 ​ − 1 ​
Since we cannot have a negative answer, we must cancel out the other answer, which I did not include.
Hope this helped! :)
~Cam943, Junior Moderator

Answered by Cam943 | 2024-06-10

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

Answered by jydclix | 2024-06-10

The width of the rectangular mural is approximately 7.09 feet, while the length is approximately 23.27 feet. This was determined by setting up an equation based on the area of the rectangle and solving a quadratic equation. The length is 2 feet more than three times the width.
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Answered by Cam943 | 2024-12-26