The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other. The ar
1 answer:
Answer
Find out the original side length of the square .
To prove
Let us assume that the original length of the square be x.
Formula
As given
The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.
Length becomes = x + 8
Breadth becomes = x -3
The area of the resulting rectangle is 126 in²
Put in the formula
(x + 8) × (x - 3) = 126
x² -3x + 8x -24 = 126
x ²+ 5x = 126 +24
x² + 5x - 150 = 0
x² + 15x - 10x - 150 = 0
x (x + 15) -10 (x +15) =0
(x + 15)(x -10) =0
Thus
x = -15 , 10
As x = -15 (Neglected this value because the side of the square cannot be negative.)
Therefore x = 10 inches be the original side of the square.
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The answer is 6.7 mi.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.
Since the right triangle is present, to calculate this we will use the Pythagorean theorem. According to the Pythagorean theorem, the square of the hypotenuse (c²) is equal to the sum of the squares of two other sides (a² + b²)<span>:
c</span>² = a² + b²<span>
First, we need to express symbols:
b - side of the right triangle (distance </span><span>between police department and Freeport High School).
a1 - </span>side of the first right triangle (distance between library and Freeport High School).<span>
a2 - </span><span>side of the second right triangle (distance between park and Freeport High School).
c1 - hypotenuse of the first triangle (distance between </span>police<span> department and library).
c2 - </span>hypotenuse of the second triangle (distance between police<span> department and park).
Therefore, we need to calculate c2.
It is given:
a2 = 6 mi
a1 = 4 mi
c1 = 5 mi
First, let's calculate b, which is a common side for two triangles:
</span>c1<span>² = a1² + b²
</span>b² = c1<span>² - a1²
</span>b² = 5<span>² - 4²
</span>b² = 25<span> - 16
</span>b² = 9
√b² = √9
b = 3.
We know b, now we can calculate c2:
c2<span>² = a2² + b²
</span>c2<span>² = 6² + 3²
</span>c2<span>² = 36 + 9
</span>c2<span>² = 45
</span>√c2<span>² = </span>√45
c2 = 6.7
The distance between police department and park is 6.7 miles.