# ACT Math: Triangles Chapter Exam

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#### Question 1 1. A triangle has side lengths 0.3, 0.4, and 0.5. Do these side lengths form a Pythagorean Triple?

#### Question 2 2. If the hypotenuse of a 30-60-90 triangle is 18, approximately how long is the short leg?

#### Question 3 3. What type of triangle is pictured below?

#### Question 4 4. If the short leg of a 30-60-90 triangle is 6, approximately how long is the hypotenuse?

#### Question 5 5. Josh claims that these triangles are similar by SSS. Do you agree or disagree with Josh?

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#### Question 6 6. What is the area of the pictured triangle?

#### Question 7 7. Brad places a marker on the ground 10 ft. away from the base of a tree at a botanical garden. He walks back towards the tree until he is standing 4 ft. away from the marker, and he is 6 ft. tall. Assuming that the top of Brad's head, the top of the tree, and the marker form two simliar triangles, how tall is the tree?

#### Question 8 8. Susan leaves her house and walks 12 miles north. Then she turns and walks x miles west. When she's done walking, the distance between her and her house in a straight line is 15 miles. How many miles did she walk west?

#### Question 9 9. Sergeant Ketchup's billiards room is 15 feet wide and 25 feet long. How many square feet is the room in total?

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Question 10
10.
In the right triangle pictured below, what is the value of angle *x*?

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#### Question 11 11. You are standing at the point (2,3) on a graph. Which point is closer: (-1,2) or (4,6)?

#### Question 12 12. Jerry wants to buy a TV online, but the ad for the TV he wants to buy does not say what the screen size is. He knows that TV screens are measured diagonally. This image shows the length and width of the screen, so he decides to use the Pythagorean Theorem to determine the diagonal screen size. What is the screen size of the TV that Jerry wants to buy (to the nearest inch)?

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Question 13
13.
Triangle POX has a perimeter of 15 inches. Side PO is 2 less than *x*, an unknown number. Side OX is 2 greater than *x*, and side PX can be expressed as 2*x* - 5. Find the length of each side of triangle POX (in the order PO, OX, PX).

#### Question 14 14. What's wrong with this triangle?

#### Question 15 15. Given triangles DAR and KMR. What is the value of y?

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#### Question 16 16. Is triangle ABC similar to triangle DEF?

#### Question 17 17. Greg is standing next to a 40 ft. tree. The sun casts a 5 ft. shadow of Greg, who is 6.4 ft. tall. How long is the tree's shadow?

#### Question 18 18. Which of the following is true?

#### Question 19 19. What is the area of the pictured rectangle?

#### Question 20 20. If a cookie sheet holds 6 cookies along one side and 4 cookies along the other, how many cookies can it hold in total?

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#### Question 21 21. Nicole wants to frame a photograph of her daughter. If the photograph has a height of 12 inches and a width of 9 inches, calculate the perimeter of the frame needed to frame the entire photograph?

#### Question 22 22. In the picture shown below, there are three lines marking each side of the triangle. These lines give the indication that the triangle is:

#### Question 23 23. The hypotenuse of a right triangle is 30. The lengths of the two shorter sides are x and x + 10. Is this a 3-4-5 right triangle?

#### Question 24 24. Study the given diagram. Find the value of x, the distance between T and E.

#### Question 25 25. If the leg of a 45-45-90 triangle is 19, approximately how long is the hypotenuse?

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Question 26
26.
Rectangle HYGT has a perimeter of 170 inches. If the length is 10*x* - 7 and the width is 6*x* + 12, how wide is the rectangle?

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Question 27
27.
The isosceles triangle pictured below shows one angle measuring 40 degrees. What is the measure of angle *x*?

#### Question 28 28. A right triangle has one leg that measures 7 inches, and the second leg measures 10 inches. How long is the hypotenuse?

#### Question 29 29. A flat screen television has a 50 inch diagonal and a height of 25 inches. How wide is the television?

#### Question 30 30. Determine if triangle VEZ is similar to triangle MAG.

#### ACT Math: Triangles Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!