The diagonals of rectangle nopq intersect at point r. if qr=3x-4 and np=5x+20, solve for x.
2 answers:
Answer:
The value of "x" is 28.
Step-by-step explanation:
As can see in the attach the length of both diagonals is the same. From the problem, you have the length of segment qr = 3x -4, which represents half of the diagonal. Then, length of segment np = 5x + 20, is the completa diagonal. So, you have to multiply the equation for qr by 2 and then equal it to equation of segment np.
2·(3x - 4) = 5x + 20 ⇒ 6x - 8 = 5x + 20 ⇒ 6x - 5x = 20 + 8 ⇒ x = 28.
Summarizing the value of "x" is 28.
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Answer:
Part 1)
Part 2)
a)
b)
c)
Step-by-step explanation:
<u><em>The complete question in the attached figure</em></u>
Part 1) Write an expression for the perimeter of the shape
we know that
The figure is composed by a larger square, a rectangle and a smaller square
1) The area of the larger square is given
so
The length and the width of the larger square is x units
2) The area of the rectangle is given
so
The length of the rectangle is x units and the width is 1 unit
3) The length and the width of the smaller square is x units
see the attached figure N 2 to better understand the problem
Find out the perimeter
The perimeter is the sum of all the sides.
so
Part 2) Find the perimeter for each of the given values of x.
a) For x=7 units
Substitute the value of x in the expression of the perimeter
b) For x=5.5 units
Substitute the value of x in the expression of the perimeter
b) For x=7/3 units
Substitute the value of x in the expression of the perimeter
