The diagram below shows a rectangle with dimensions in cm 3x+7y 3x+4y-4 8x+4y+2 7x+ y
3 answers
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assumin the sides are listed in sequence, the two parallel sides must be congruent. So that means we have
3x+7y = 8x+4y+2
3x+4y-4 = 7x+ y
solving that gives
x = 2 and y = 4
so the rectangle is 34 by 18
3x+7y = 8x+4y+2
3x+4y-4 = 7x+ y
solving that gives
x = 2 and y = 4
so the rectangle is 34 by 18
That is correct. Given the equations
3x+7y = 8x+4y+2 ...(1)
3x+4y-4 = 7x+y ...(2)
Simplifying equation (1), we have
3x-8x = 4y-7y+2
-5x = -3y+2
5x = 3y-2 ...(3)
Simplifying equation (2), we have
3x-7x = y-4y+4
-4x = -3y+4
4x = 3y-4 ...(4)
Solving equations (3) and (4) simultaneously, we get
x = 2 and y = 4
Substituting these values back into equation (1) or (2), we can indeed find that both equations are satisfied. Therefore, the dimensions of the rectangle are 34 cm by 18 cm.
3x+7y = 8x+4y+2 ...(1)
3x+4y-4 = 7x+y ...(2)
Simplifying equation (1), we have
3x-8x = 4y-7y+2
-5x = -3y+2
5x = 3y-2 ...(3)
Simplifying equation (2), we have
3x-7x = y-4y+4
-4x = -3y+4
4x = 3y-4 ...(4)
Solving equations (3) and (4) simultaneously, we get
x = 2 and y = 4
Substituting these values back into equation (1) or (2), we can indeed find that both equations are satisfied. Therefore, the dimensions of the rectangle are 34 cm by 18 cm.