Rectangle X measures 7 cm by \((x+1)\) cm. Rectangle Y has dimensions of \((3x+6)\) cm and 4 cm. The area of rectangle X is half the area of rectangle Y. Calculate the lengths of the sides of the rectangles and, hence, their areas.

lengthxwidth=area and rectangle Y/B is twice as big as X so
7(x+1)=1/2(4)(3x+6) 7x+7=1/2(12x+24) x=5
Rectangle X=7(5+1)=42 Rectangle Y=4(3*5+6)=84
84 is twice as big as 42 :D

Answered by cjbuckleyuk | 2024-06-10

The dimensions of Rectangle X are length = 7 cm and width = 6 cm. Its area is 42 square cm. For Rectangle Y, the dimensions are length = 21 cm and width = 4 cm, resulting in an area of 84 square cm.
Let's first find the dimensions of Rectangle X:
Given that the length of Rectangle X is 7 cm and the width is (x + 1) cm, we have:
Length (X) = 7 cm
Width (X) = (x + 1) cm
Next, let's find the dimensions of Rectangle Y:
The length of Rectangle Y is (3x + 6) cm and the width is 4 cm, so:
Length (Y) = (3x + 6) cm
Width (Y) = 4 cm
According to the problem, the area of Rectangle X is half the area of Rectangle Y. Therefore, we can set up the following equation:
Area (X) = 0.5 * Area (Y)
Substituting the area formulas, we get:
7(x + 1) = 0.5 * [(3x + 6) * 4]
Solving for x:
7x + 7 = 6x + 12
x = 5
With x = 5, we can find the dimensions and areas of the rectangles:
For Rectangle X:
Length (X) = 7 cm
Width (X) = (5 + 1) cm = 6 cm
Area (X) = Length (X) * Width (X) = 7 cm * 6 cm = 42 square cm
For Rectangle Y:
Length (Y) = 3(5) + 6 = 15 + 6 = 21 cm
Width (Y) = 4 cm
Area (Y) = Length (Y) * Width (Y) = 21 cm * 4 cm = 84 square cm
To learn more about Rectangle
https://brainly.com/question/25292087
#SPJ2

Answered by bamkinbose | 2024-06-18

Rectangle X measures 7 cm by 6 cm with an area of 42 square cm, while Rectangle Y measures 21 cm by 4 cm with an area of 84 square cm. The value of x found is 5. The areas are in the expected ratio of half as given in the problem description.
;

Answered by bamkinbose | 2024-11-27