Answer:
Explanation:
Let x be the length and y be the width
The length is 1 inch longer than the width
So : x-1 =y
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The diagonal is 5 inches
The diagonal, width and length are forming a right triangle where the diagonal is the hypotenus
The Pythagorian theorem:
x^2 + y^2 = 5^2
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Let's calculate y the width
The system is :
x-1 = y => x =y+1
x^2 + y^2 = 25
Replace x in the second equation with y+1 :
(y+1)^2 + y^2 = 25
y^2 + 2y + 1 + y^2 = 25
2y^2 + 2y +1 = 25
2y^2 + 2y -24 = 0
This is a quadratic equation so we will use the discriminant
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the discriminat is b^2-4ac
● b =2
● a = 2
● c = -24
b^2 -4ac = 4-4*2(-24) =196 > 0
Since the dicriminant is positive this equation has two solutions y and y'
y = (-2-14)/4 = -16/4 = -4
y '= (-2+14)/4 = 12/4 = 3
The first solution is negative
A distance is always positive so the first solution can't be the width
Then the width is 3