Please help me! I'm having some difficulty with these problems. Any help would suffice. Thank you!
1: How many non-congruent right triangles with legs of integral lengths have a hypotenuse of length 10?
a) 1
b) 2
c) 3
d) 4
e) More than 4
2: If an equilateral triangle has an area of √3, then which of the following is its perimeter?
a) 3
b) 5
c) 6
d) 9
e) 15
3: The ratio of the lengths of the hypotenuses of two similar right triangles is 1 to 2. What is the ratio of the triangles’ perimeters?
a) 1 to 2
b) 1 to 3
c) 1 to 4
d) 1 to 8
e) Cannot be determined.
4: What is the perimeter of an equilateral triangle with an altitude of 4√3?
a) 4
b) 6
c) 12
d) 18
e) 24
5: If an equilateral triangle has sides of length x, (x/3)+6, and (x/9)+8, what is its perimeter?
a) 9
b) 12
c) 18
d) 27
e) Not enough information given
6: Two right triangles are similar. One of them has a hypotenuse of a and an area of b^2. The other has a hypotenuse of c. What is the second triangle’s area?
a) (ab^2)/c
b) (cb^2)/a
c) (b^2•c^2)/a^2
d) (a^2•b^2)/c^2
e) a^2•b^2•c^2
1: How many non-congruent right triangles with legs of integral lengths have a hypotenuse of length 10?
a) 1
b) 2
c) 3
d) 4
e) More than 4
2: If an equilateral triangle has an area of √3, then which of the following is its perimeter?
a) 3
b) 5
c) 6
d) 9
e) 15
3: The ratio of the lengths of the hypotenuses of two similar right triangles is 1 to 2. What is the ratio of the triangles’ perimeters?
a) 1 to 2
b) 1 to 3
c) 1 to 4
d) 1 to 8
e) Cannot be determined.
4: What is the perimeter of an equilateral triangle with an altitude of 4√3?
a) 4
b) 6
c) 12
d) 18
e) 24
5: If an equilateral triangle has sides of length x, (x/3)+6, and (x/9)+8, what is its perimeter?
a) 9
b) 12
c) 18
d) 27
e) Not enough information given
6: Two right triangles are similar. One of them has a hypotenuse of a and an area of b^2. The other has a hypotenuse of c. What is the second triangle’s area?
a) (ab^2)/c
b) (cb^2)/a
c) (b^2•c^2)/a^2
d) (a^2•b^2)/c^2
e) a^2•b^2•c^2
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1) a) 1
This is a variation of 3, 4, 5 triangle, except this one has sides 6, 8, and 10. Only a triangle with these lengths fit the description.
2) c) 6
The area of an equilateral triangle with side s is s² * (√(3)/4). Set this equal to √(3), which is the area of the given triangle. Solve for s, the side.
s² * (√(3)/4) = √(3)
s² = √(3) * (4/√(3)) = 4
s² = 4
s = 2
If each side is 2, then the perimeter is 6
3) a) 1 to 2
If the triangles are similar, then all of the sides are similar in a ratio of 1: 2. Thus the perimeter is also similar in this ratio. If this asked for the similarity of the area, then it would be 1 : 4, since you are multiplying two sides. You have to square the ratio in that case.
4) e) 24
The altitude of an equilateral triangle is s√(3)/2, where s is the side. Set this equal to 4√(3), the altitude given and solve for s.
This is a variation of 3, 4, 5 triangle, except this one has sides 6, 8, and 10. Only a triangle with these lengths fit the description.
2) c) 6
The area of an equilateral triangle with side s is s² * (√(3)/4). Set this equal to √(3), which is the area of the given triangle. Solve for s, the side.
s² * (√(3)/4) = √(3)
s² = √(3) * (4/√(3)) = 4
s² = 4
s = 2
If each side is 2, then the perimeter is 6
3) a) 1 to 2
If the triangles are similar, then all of the sides are similar in a ratio of 1: 2. Thus the perimeter is also similar in this ratio. If this asked for the similarity of the area, then it would be 1 : 4, since you are multiplying two sides. You have to square the ratio in that case.
4) e) 24
The altitude of an equilateral triangle is s√(3)/2, where s is the side. Set this equal to 4√(3), the altitude given and solve for s.
12
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