Example Question - missing side length
Here are examples of questions we've helped users solve.
Finding Missing Side Length in Similar Triangles
The image shows two similar triangles, and we're asked to find the missing side length, labeled as "x". When two triangles are similar, corresponding side lengths are proportional. In the image, the smaller triangle has sides of length 4 and "x", and the larger triangle has corresponding sides of length 8 and 16. We can set up a proportion using the known side lengths of the triangles: \[\frac{x}{16} = \frac{4}{8}\] To find x, we solve for it by cross-multiplying: \[8x = 4 \times 16\] \[8x = 64\] \[x = \frac{64}{8}\] \[x = 8\] Therefore, the missing side length "x" is 8 units long.
Solving for Missing Side Length in Similar Triangles
To solve for the missing side length in similar triangles, we can set up a proportion based on the corresponding sides of the triangles. Let's call the missing side length "x". For the smaller triangle, we have the sides as x (the one we want to find) and 8. For the larger triangle, the corresponding sides are 7 and 16. Setting up our proportion, we get: x/7 = 8/16 Now we want to solve for x: x = (8/16) * 7 x = (1/2) * 7 x = 7/2 x = 3.5 So the missing side length is 3.5 units.
Solving for Missing Side Length of Similar Triangles
The triangles in the image are similar, which means their corresponding sides are proportional. From the image, we can set up a ratio of the corresponding sides of the two similar triangles. Let's denote the unknown side length of the smaller triangle as \( x \). We are given the sides of the larger triangle as 8 and 16. Since the triangles are similar, the ratio of the sides of the smaller triangle to the larger one should be the same. So we have: \[\frac{x}{8} = \frac{7}{16}\] Now we can solve for \( x \) by cross-multiplying: \( 16x = 8 \times 7 \) \( 16x = 56 \) Now, divide both sides by 16 to find \( x \): \( x = \frac{56}{16} \) \( x = 3.5 \) Therefore, the missing side length of the smaller triangle is 3.5 units.
Solving for Missing Side Length in Similar Triangles
To solve for the missing side length, we can use the property that corresponding sides of similar triangles are proportional. The corresponding sides of the triangles are in proportion, so we can set up the following equation: \[ \frac{x}{8} = \frac{8}{16} \] Now solve for \( x \): \[ x = \frac{8 \times 8}{16} \] \[ x = \frac{64}{16} \] \[ x = 4 \] Therefore, the missing side length \( x \) is 4 units.
Finding Missing Side Length in Right Triangle using Pythagorean Theorem
The Pythagorean theorem is used to find the length of a side of a right triangle. It states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as: a² + b² = c² Here, c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides. From the image, the hypotenuse of the triangle is 17 inches, and one of the other sides is 8 inches. We need to find the length of the missing side, labeled b. Using the Pythagorean theorem: 8² + b² = 17² 64 + b² = 289 Now, subtract 64 from both sides to isolate b²: b² = 289 - 64 b² = 225 Taking the square root of both sides gives us the length of the missing side: b = √225 b = 15 Therefore, the length of the missing side b is 15 inches.
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