The length of the diagonals of a rectangle are represented by 8x+3 feet and 4x+7 feet. Find the length of each diagonals
As they both are the diagonals of a same rectangle, they would be equal.
8x + 3 = 4x + 7
8x - 4x = 7 - 3
4x = 4
x = 4/4
x = 1
So, 1st diagonal = 8(1)+3 = 11
2nd diagonal = 4(1)+7 = 11
In short, Your Answer would be 11 feet
Hope this helps!
You can use the fact that both of the diagonals of a rectangle are of same length.
The length of each diagonal is 11 feet
In a quadrilateral(a closed figure made by 4 straight line segments joined end to end), if we join the unconnected vertices(the intersection of line segments), then two new lines come in middle. These two lines are called diagonals.
The length of both the diagonals of a rectangle are same.
Since both the diagonals are of same length, we have:
\(8x + 3 = 4x + 7\\\\\text{Subtracting 4x on both sides}\\\\8x - 4x + 3 = 4x - 4x + 7\\4x + 3 =7\\\\\text{Subtracting 3 on both side and then dividing by 4 on both sides}\\4x + 3 = 7 - 3\\4x = 4\\\\\dfrac{4x}{4} = \dfrac{4}{4}\\\\x = 1\)
Thus, the length of diagonals are:
\(8x + 3 = 8 \times 1 + 3 = 11\\4x + 7 = 4 \times 1 + 7 = 11\)
Thus, both diagonals are of 11 feet.
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