Which set of ordered pairs represents a function?
1 answer:
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Answer:
The lengths of sides of squares are 5 cm and 9 cm.
Step-by-step explanation:
Let the sides of rectangle be x and y .
Area of rectangle = Length × Breadth
Given : Area of rectangle = 45 cm².
⇒ x × y = 45
⇒ ........(1)
Two squares are constructed such that two adjacent sides of the rectangle
so squares have side x and y .
Area of square = side × side
Area of square with side x = x²
Area of square with side y = y²
Also, The combined area of the two squares is 106 cm².
⇒ x² + y² = 106
From (1) put value of x , we get,
Solving for y ,
or
on solving we get y = 5 and y = 9
Also, x can be find by putting in (1),
⇒ and ⇒
⇒ x = 9 and x = 5
Thus, lengths of sides of squares are 5 cm and 9 cm.
Answer:
Step-by-step explanation:
The octagon is irregular, meaning not all sides have equal length. However, we can break it up into other shapes to find the area.
The octagon shown in the figure is a composite figure as it's composed of other shapes. In the octagon, let's break it up into:
- 4 triangles (corners)
- 3 rectangles (one in the middle, two on top after you remove triangles)
<u>Formulas</u>:
- Area of rectangle with length
and width
:
- Area of triangle with base
and height
:
<u>Area of triangles</u>:
All four triangles we broke the octagon into are congruent. Each has a base of 2 and a height of 2.
Thus, the total area of one is
The area of all four is then units squared.
<u>Area of rectangles</u>:
The two smaller rectangles are also congruent. Each has a length of 3 and a width of 2. Therefore, each of them have an area of units squared, and the both of them have a total area of
units squared.
The last rectangle has a width of 7 and a height of 3 for a total area of units squared.
Therefore, the area of the entire octagon is