These two scalene triangles are similar with a scale of 4:5. What is true about these figures?
2 answers:
Alright, lets get started.
Lets check each possible answer one by one.
We will start from option B.
BC is from small triangle and its corresponding side is DF, so its ratio will be not
as given in option. Hence option B is incorrect.
For option C,
Angle a° and angle f° are not similar angles, if they were similar, then only their ratio will be 1 otherwise not 1. Hence option C is incorrect.
For option D,
Angle c° and angle f° are similar angles so, their ratio will be . Hence option D is incorrect.
Now option A,
ED and AB are corresponding sides. ED is from bigger triangle and AB is from smaller triangle. Their ratio will be . Hence option A is correct answer.
Hope it will help :)
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Answer:
The perimeter and area of the square are 56 units and 196 square units, respectively.
Step-by-step explanation:
The inner right triangle represents a 45-45-90 right triangle, which has the feature of a hypotenuse whose length is time the length of any of its legs. If the hypotenuse has a measure of
, then the legs of the triangle have a measure of
.
Now, we are aware that the side length of the square is twice the length of the leg of the right triangle. Then, side length of the square is 14 units long.
Lastly, we know from Geometry that the perimeter and area of the square are represented by the following expressions:
Perimeter
(1)
Area
(2)
Where is the side length of the square.
If we know that , then the perimeter and area of the square are, respectively:
The perimeter and area of the square are 56 units and 196 square units, respectively.