find the length x in the figure a shape like a shoe with x on top, 10 cm to the height, 6cm on the lace shoes and x in the front shoes.the area of the shaded region is given 144 cm square.
Amira is solving the equation x2 – 6x = 1. Which value must be added to both sides of the equation to make the left side a perfect-square trinomial?
To find the length x in the figure, we first need to understand the shape. Based on your description, it seems like a shoe shape with a height of 10 cm, 6 cm on the lace shoes, and x on the front shoes. We are also given that the area of the shaded region is 144 cm².
To solve this, we can break the shape into two parts: the rectangle representing the lace shoes and the triangle representing the front shoes.
1. The area of the rectangle:
The base of the rectangle is the length x, and the height is given as 6 cm. So the area of the rectangle is calculated as: Area = base × height = x × 6 cm.
2. The area of the triangle:
The base of the triangle is again the length x, and the height is given as 10 cm. So the area of the triangle is: Area = 0.5 × base × height = 0.5 × x × 10 cm.
Now, we add the area of the rectangle and the triangle to find the total shaded area, which is given as 144 cm²:
144 cm² = Area of rectangle + Area of triangle
144 cm² = x × 6 cm + 0.5 × x × 10 cm
Simplifying the equation:
144 cm² = 6x + 5x
144 cm² = 11x
x = 144 cm² / 11 ≈ 13.09 cm
Therefore, the length x in the figure is approximately 13.09 cm.