Question 909362: Thank you for helping me! There are three questions on my homework which I have tried and failed could you please help me with them.
Question one is: Rectangle A has one side which is 6cm long and the other is (x+2)cm long. Rectangle B has sides of length (2x+1)cm and 3cm. If the perimeters are the same, calculate the value of x and hence, the lengths of the sides of the triangles.
I have tried to work out this question, making x four but this does not work as it gives me sides of 6 and 6 on triangle A.
My Second question is that: Rectangle X measures 7cm by (x+1)cm. Rectangle b has dimensions of (3x+6)cm and 4cm. The area of rectangle X is half the area of rectangle B. Calculate the lengths of the sides of the rectangles and their areas. (Please reply as soon as possible, thanks)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! perimeter = 2L + 2W, where L = length and W = width.
In rectangle A this becomes 2*6 + 2*(x+2)
in rectangle B, this becomes 2*3 + 2*(2x+1)
simplify each expression and you get:
perimeter of A = 16 + 2x
perimeter of B = 8 + 4x
since the perimeters are equal, you get 16 + 2x = 8 + 4x
solve for x in this equation and you get x = 4
when x = 4, the perimeter of A is 24 and the perimeter of B is 24.
in your second problem, area of a rectantgle is equal to L*W, where L = length and W = width.
area of rectangle X is equal to 7 * (x+1)
area of rectangle B is equal to 4 * (3x + 6)
the area of rectangle X is equal to 1/2 * the area of rectangle B.
You get:
7 * (x+1) = 1/2 * 4 * (3x + 6)
simplify to get 7x + 7 = 6x + 12
solve for x in this equation to get x = 5
when x = 5:
area of rectangle X is equal to 7 * (x+1) becomes 7 * 6 which becomes 42.
area of rectangle B is equal to 4 * (3x + 6) becomes 4 * 21 which becomes 84.
since 42 is equal to 1/2 * 84, the equations confirm the solution of x = 5 as good.
i'm assuming you know how to simplify and how to solve equations so i didn't give you the details of how the results were obtained.
if you don't understand how i got the answers, then let me know and i'll guide you through it.
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