SOLUTION: The width of a rectangular painting is 10 in. less than the length. The area of the painiting is 96in square. Find the length and width.

Algebra ->  Surface-area -> SOLUTION: The width of a rectangular painting is 10 in. less than the length. The area of the painiting is 96in square. Find the length and width.       Log On


   

Question 1155382: The width of a rectangular painting is 10 in. less than the length. The area of the painiting is 96in square. Find the length and width.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

if the width W of a rectangular painting is 10in less than the length L, we have
W=L-10......eq.1
if the area of the painting is 96in%5E2, we have
W%2AL=96..........substitute W from eq.1
%28L-10%29%2AL=96.......solve for L
L%5E2-10L=96
L%5E2-10L-96=0.....factor completely
L%5E2%2B6L-16L-96=0
%28L%5E2%2B6L%29-%2816L%2B96%29=0
L%28L%2B6%29-16%28L%2B6%29=0
%28L+-+16%29+%28L+%2B+6%29+=+0
take only positive solution for length
%28L+-+16%29++=+0=> L+=16in

go to eq.1
W=L-10......eq.1, substitute L
W=16-10
W=6in

answer:
the length is 16in and the width is 6in


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

The width of a rectangular painting is 10 in. less than the length. The area of the painiting is 96in square. Find the length and width.
This is just two FACTORS of 96 with a difference of 10, which are: highlight_green%28matrix%281%2C3%2C+6%2C+and%2C+16%29%29

That's ALL!!