Miscellaneous
(more difficult)
(more difficult)
A yardstick is stood perpendicular to the ground. Its shadow is 12ft. In order for the sum of the length of a different object's shadow and its height to be 25ft, what is this object's height in inches?
60in
In proportion a/b = c/d, which variables are the extremes and which are the means.
Extremes - a and d
Means - b and c
There are three ways to show a ratio. What are these ways? Use the variables a and b.
a to b
a:b
a/b
What are the three theorems that can prove triangle similarity?
Angle-Angle
Side-Side-Side
Side-Angle-Side
What is the sum of the squares of the answers to the following proportions:
x/35 = 29/7
y/17 = 15/68
Provide your answer as a decimal.
21039.0625
Which property states that in proportion a/b = c/d, ad = bc?
Cross Products Property
Quadrilaterals ABCD and WXYZ are squares. If the similarity ratio of square ABCD to square WXYZ is 1:2, what is the area of square WXYZ if the area of square ABCD is 8cm2?
32cm2
Triangles ABC and ADF are similar. Their points are as follows: A(0,5), B(1,0), C(7,2), D(2,-5) and F(14,-1). What is the scale factor between triangle ADF and triangle ABC?
2
What is the sum of the squares of the numbers (2,7,9, and/or 15) assigned to all similar pairs of triangles?
2) Triangles ABC and XYZ. Angles A, C, Z, and X measure 92o, 16o, 92o, and 16o, respectively.
7) Triangles DEF and UVW. Sides DE, EF, and FD measure 2mm,5mm, and 8mm, respectively. Sides UVmm, VWmm, and WU measure 14mm, 17, and 20, respectively.
9) Triangles GHI and RST. Angles G, H, T, and S measure 17o, 54o, 109o, and 54o, respectively.
15) Triangles JKL and OPQ. Sides JK, KL, LJ, OP, PQ, and QO measure 2mm, 4mm, 7mm, 6mm, 12mm, and 21mm, respectively.
306
Solve the following proportion: 15/x = 2(x+2)/2.
x = 3
Triangles ABC and XYZ have a similarity ratio of 1:3. The lengths of sides AB, BC, and CA are 8m, 5m, and 11m, respectively. The measures of angles A and C are 24.62° and 41.802°, respectively. What is the sum of the measures of side length XY and angle Z?
65.802
Triangle XYZ has coordinates X(4,6), Y(1,8), and Z(2,2). Between this triangle and triangle X'Y'Z' there is a scale ratio of 1:3. What is the sum of the new x-digits multiplied by the sum of the new y-digits?
1008
Points A, B, and C lie along the perimeter of triangle XYZ. The incenter of triangle XYZ is located at the point of concurrency of lines AX, BY, and CZ. Sides XY and XZ measure 4km and 6km, respectively. YA measures 2km. What is the perimeter of this triangle? Provide units.
15km
Triangle ABC is split by line DE, which lies parallel to side BC. DE measures 6.987, BC measures 23.243in, AD measures 4in, AE measures 9in, and BE measures 21in. What is the perimeter of this triangle, rounded to the nearest tenth? Provide units.
66.6in
The ratio of u to v is 2:7, the ratio of v to w is 3:5, the ratio of w to x is 9:4, the ratio of x to y is 17:1, and the ratio of y to z is 2:3. If u is 17, what is z? Provide your answer as a fraction.
Note: 17 is a prime factor of 272 and 459
3 8/9 (three and eight-ninths)
[u - 17
u:v - 59 1/2
v:w - 99 1/6
w:x - 44 2/27
x:y - 2 16/27
y:z - 3 8/9]
The similarity ratio between rectangles ABCD and WXYZ is x. What is x if the sum of the similarity ratio, the perimeter ratio, and the area ratio is 35?
5
The height of trapezoid ABCD is 5cm. The bases of the trapezoid are AB and CD. In trapezoid ABCD, point Y is the midpoint of line AC and point Z is the midpoint of line BC. Points H and E lie upon the trapezoid's perimeter. The perimeter of square ABFG is 16cm. A perpendicular line from trapezoid base CD to Vertex F of square ABFG is 1cm. Side FG of this square lies upon line EH. EY, AY, and ZB measure 2cm, 3cm, and 14cm, respectively. What is the sum of ZH, EC and ZD? Provide units.
24 1/3 (twenty four and one-third)cm
On the coordinate plane, there are six points, U(4,7), V(-3,2), W(0,-5), X(8,2), Y(1,3), and Z(-10,-1). Find the ratios expressing the slopes of lines UZ, VY, and WX, labelled a, b, and c, respectively. Then, if the ratio of a to c is proportional to the ratio of b to x, what is the value of x2 - x?
-(1/4)
The ratio of the side lengths of a hexagon is 1:2:3:4:5:6. If the ratio between x and y is 7:1 and x = 14, then the perimeter of this hexagon can be represented by the equation 2[y5 - (x - y) + 1]. Using this equation, solve for the third smallest side length and change the ratio between x and y to this side length:1. Using this new ratio, what would a have to be for the perimeter of this hexagon to equal a[y5 - (x-y) + 1], if x = 6?
-14
The scale factor between a building and its model is 11:1. The model measures 29cm by 7cm by x. The value of x is the remainder after the sum of the model's two provided side lengths is divided by the sum of the two calculable side lengths of the building. What is the combined volume of both the model and the actual building? Provide your answer in terms of meters cubed.
9726948.007308m3