The following triangle is isosceles. Write an equation and use it to solve for x.
2 answers:
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Answer: For the figure on the left {c}, the Area is 30m (squared) and the Perimeter is 46m.
For the figure on the right {d}, the Area is 32cm (squared) and the Perimeter is 34cm
Step-by-step explanation: (Please refers to the attached diagram)
We shall start with the diagram on the left. The first thing is to break it down into regular shapes, such as rectangles, squares, etc. The dotted line that runs from point C to point G divides the figure into two rectangles which are ABCG {or X} and GDEF {or Y}. Line AG measures 10m since it’s the same length as line BC. Similarly line GF measures 2m since it’s the same length as line DE. So rectangle “X” has dimensions;
L = 10, W = 1
Area of a rectangle = L x W
Area = 10 x 1
Area = 10m
Similarly rectangle Y has dimensions L= 10m and W = 2m
Hence area of rectangle “Y” is computed as
Area = L x W
Area = 10 x 2
Area = 20m
Area of the entire figure is derived as
Area of rectangle X + Area of rectangle Y, which is
10m + 20m = 30m {squared)
The perimeter of rectangle X is given as Perimeter = 2(L + W)
Perimeter = 2(10 + 1)
Perimeter = 2(11)
Perimeter = 22m
Also, perimeter of rectangle Y is derived as
Perimeter = 2(L + W)
Perimeter = 2(10+ 2)
Perimeter = 2(12)
Perimeter = 24m
Therefore the perimeter of the entire figure is derived as
Perimeter of rectangle X + perimeter of rectangle Y, which is
22m + 24m and that equals 46m
For the second figure on the right side of the page, we shall also break it down with the dotted lines that runs from point E to point G. That leaves us with rectangle ABGF {or P} and rectangle EGCD {or Q}.
Rectangle “P” has dimensions L= 4 and W = 2
Area of rectangle P = 4 x 2
Area of rectangle P = 8cm
Similarly area of rectangle Q is given as Area of Q = 8 x 3
Area of Q = 24cm
Area of the entire figure is derived as
Area of P + Area of Q,
8cm + 24cm
= 32cm {squared}
To compute the perimeter of rectangle P
Perimeter of a rectangle = 2(L + W)
Perimeter of rectangle P = 2(4 + 2)
Perimeter of rectangle P = 2(6)
Perimeter of rectangle P= 12cm
Similarly Perimeter of rectangle Q = 2(L + W)
Perimeter of rectangle Q = 2(8 + 3)
Perimeter of rectangle Q = 2(11)
Perimeter of rectangle Q = 22cm
Hence, perimeter of the entire figure is derived as perimeter of rectangle P + perimeter of rectangle Q which equals
12cm + 22cm and that equals
34cm.
