Solve for x
x/5 = 20/x
x=10
A proportion is a statement that two ratios are equal.
True
In the proportion x/12= 3/4, what is the value of x?
A) 4
B) 6
C) 9
D) 36
C
If the ratio of two numbers is 4:7 and their sum is 88, what is the smaller number?
B
x + 5/10 = x - 1/4
x = 5
If the cross-products of two ratios are equal, then the ratios form a proportion.
TRUE. This is the Fundamental Property of Proportions (ad = bc).
Which of the following defines a proportion?
A) The product of two numbers.
B) A statement that two ratios are equal.
C) The difference between two fractions.
D) A ratio compared to a percentage.
B. A proportion is mathematically defined as the equality of two ratios.
Find the value of $x$ in the proportion 3/x = x/27.
x2 = 3x27 x2 = 81. The square root of 81 is 9.
(x + 2)/4 = 9/6
x = 4
If two triangles are similar, their corresponding sides are congruent.
Which of the following pairs of ratios forms a true proportion? A) 2/3 and 4/9
B) 3/5 and 12/20
C) 1/4 and 5/15
D) 7/8 and 14/15
B 3x20 = 60 and 5x12 = 60. Since the cross-products are equal, it is a true proportion.
Leonardo da Vinci created a famous drawing of a man with arms and legs outstretched in a circle and a square. This drawing, called the Vitruvian Man, was designed to show that the human body is a masterpiece of proportional geometry.
According to da Vinci’s notes on the drawing, what is the proportion between a person's height and their arm span (the distance from fingertip to fingertip)?
The arm span is exactly equal to the height.
3/(x - 1) = 15/20
x = 5
All equilateral triangles are similar to each other.
TRUE Since all their angles are $60°$, they always satisfy the AA Similarity Postulate.
Which of the following is NOT a valid theorem to prove that two triangles are similar? A) AA (Angle-Angle)
B) SAS (Side-Angle-Side)
C) SSS (Side-Side-Side)
D) SSA (Side-Side-Angle)
D Similarity Postulates: AA, SAS, and SSS are proven ways to show triangles are similar. SSA is not a valid theorem because it does not guarantee a unique shape.
Have you ever noticed that school paper (like A4 or long bond paper) always seems to have a similar shape? There is a specific reason for this! If you cut a standard piece of A4 paper in half, the two new pieces are exactly similar in proportion to the original piece.
1:√2
(2x - 5)/3 = (x + 1)/2
x = 13
The altitude drawn to the hypotenuse of a right triangle divides the triangle into two triangles that are similar to the original triangle and to each other.
TRUE. This is the Right Triangle Similarity Theorem.
In a map scale, 1 cm represents 50 km. If two cities are 7 cm apart on the map, what is their actual distance? A) 57 km B) 150 km C) 350 km D) 500 km
CSet up the proportion: 1/50= 7/x.
x = 50 x 7 = 350.
There is a specific mathematical ratio, approximately equal to 1.618, that appears frequently in nature, architecture, and art (like the Parthenon or the Mona Lisa). What is the name of this "perfect" proportion?
The Golden Ratio