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Poorly wrote this question:
a rectangle and a right angled triangle are joined together to make a total area of 108 meters squared. the side of the rectangle in contact with the triangle has length d. the total width of the shape is 12meters. the other side of the rectangle has length 12 minus d divided by 2. how long is d
Answer:
To find the length of the side of the rectangle (d) that is in contact with the right-angled triangle, you can set up an equation to represent the total area of the shape.
The area of the rectangle is equal to its length multiplied by its width, and the area of the right-angled triangle is equal to one half of the product of its base and height. Let x be the length of the rectangle and y be the width of the rectangle.
Then, the total area of the shape can be represented by the following equation:
(x * y) + (0.5 * x * y) = 108
This equation simplifies to:
1.5 * x * y = 108
You can then substitute the given values for x and y to find the value of d.
1.5 * d * (12 - d / 2) = 108
3 * d * (12 - d / 2) = 216
3 * d * 12 - 3 * d^2 / 2 = 216
36 - 3 * d^2 / 2 = 216
-3 * d^2 / 2 = 180
d^2 = 120
d = 10.392305
The length of the side of the rectangle that is in contact with the right-angled triangle is approximately 10.392305 meters.
I hope this helps! Let me know if you have any other questions.