Answer:
Step-by-step explanation:
The given relation between length and width can be used to write an expression for area. The equation setting that equal to the given area can be solved to find the shed dimensions.
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<h3>Given relation</h3>
Let x represent the width of the shed. Then the length is (2x+3), and the area is ...
A = LW
20 = (2x+3)(x) . . . . . area of the shed
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<h3>Solution</h3>
Completing the square gives ...
2x² +3x +1.125 = 21.125 . . . . . . add 2(9/16) to both sides
2(x +0.75)² = 21.125 . . . . . . . write as a square
x +0.75 = √10.5625 . . . . . divide by 2, take the square root
x = -0.75 +3.25 = 2.50 . . . . . subtract 0.75, keep the positive solution
The width of the shed is 2.5 feet; the length is 2(2.5)+3 = 8 feet.
Answer: 24, 24, 47
<u>Step-by-step explanation:</u>
In order to form a triangle, the sum of two sides must be GREATER than the third side for all combinations.
a + b > c & a + c > b & b + c > a
23 + 28 = 51 which is NOT greater than 55
15 + 30 = 45 which is NOT greater than 45
8 + 17 = 25 which is NOT greater than 25
24 + 24 > 47 & 24 + 47 > 24 & 24 + 24 > 27
all combinations are true so these side lengths can form a triangle
This is a perfect square trnomial
(a+b)²=a²+2ab+b²
we see that a=5x and b=2
(5x)²+2(5x)(2)+2²=0
factor
(5x+2)²=0
set equal to zero
5x+2=0
5x=-2
x=-2/5
