Answer:
Step-by-step explanation:
The relations between length (L) and width (W) are ...
W +9 = L
LW = 486
Substituting gives ...
(W+9)W = 486
W^2 +9W -486 = 0 . . . put in standard form
(W +27)(W -18) = 0 . . . . factor
W = 18 . . . . the positive solution
The width of the rectangle is 18 inches; the length is 27 inches.
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<em>Comment on factoring</em>
There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.
486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.
Answer:
BD - AC = 0
Step-by-step explanation:
Given that:
BC = 36 , CD = 15 and BD = x
As these are forming right angled triangle,
Using Pythagorean theorem,
Taking square root on both sides
As the given shape is rectangular, the sides parallel to each other will have same values.
AB = 15 , AD = 36 and AC = x
Now,
BD - AC = 39 - 39 = 0
Hence,
BD - AC = 0
