SOLUTION: If the diagonals of a rectangle are represented by (2x2 – 8x + 17 )m and ( x2 + 2x – 7 )m, find the value of x. How long is each diagonal?

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Question 644219: If the diagonals of a rectangle are represented by (2x2 – 8x + 17 )m and ( x2 + 2x – 7 )m, find the value of x. How long is each diagonal?
Found 2 solutions by unlockmath, MathLover1:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Since we know the diagonals are equal in a rectangle we can set up this:
2x^2 – 8x + 17 = x^2 + 2x – 7
Subtract x^2, 2x and add 7:
x^2 -10x +24 =0
Factor:
(x-6)(x-4)=0
Solve for x:
x=6
x=4
We have two possible answers: 6 & 4
Make sense?
RJ
www.math-unlock.com

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The diagonals of a rectangle are congruent.

%282x%5E2-8x%2B17%29m=%28x%5E2%2B2x-7%29m

%282x%5E2-8x%2B17%29cross%28m%29=%28x%5E2%2B2x-7%29cross%28m%29

2x%5E2-8x%2B17=x%5E2%2B2x-7

2x%5E2-8x%2B17-x%5E2-2x%2B7=0

x%5E2-10x%2B24=0

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%2A1%2A24+%29%29%2F%282%2A1%29+

x+=+%2810+%2B-+sqrt%28100-96+%29%29%2F2+

x+=+%2810+%2B-+sqrt%284+%29%29%2F2+

x+=+%2810+%2B-+2%29%2F2+...find solutions

x+=+%2810+%2B+2%29%2F2+

x+=+12%2F2+

x+=+6+

or

x+=+%2810+-+2%29%2F2+

x+=+8%2F2+

x+=+4