Solving Similar Triangles

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Questions

• If DB = 24, AE = 3, and EC= 18, what is AD?
• Delroy’s sailboat has two sails that are similar triangles. The larger sail has sides of 10 feet, 24 feet, and 26 feet. If the shortest side of the smaller sail measures 6 feet, what is the perimeter of the smaller sail?
• Suppose you have triangle ABC with AB = 5, BC = 7, and CA = 10, and also triangle EFG with EF = 900, FG = 1260, and GE = 1800. Are these triangles similar, and if so, what is the scale factor?
• Triangles JKL and PML are similar. JL = 10 JK = #x# PL = 16 PM = 22. Given this information what does #x# equal?
• The angles of similar triangles are equal always, sometimes, or never?
• The smaller of two similar triangles has a perimeter of 20cm (#a+b+c=#20cm). The lengths of the longest sides of both triangles are in proportion 2:5. What is the perimeter of the larger triangle? Please explain.
• A school building has a height of 40 feet. Its shadow is currently 13.5 feet long, and the shadow of the church next door is 20.7 feet long. How would you use similar triangles to calculate the height of the church to the nearest tenth of a foot?
• Two similar triangles have a ratio of similarity of 2:3. If the perimeter of the second triangle is 15 inches, what is the perimeter of the first triangle?
• The perimeters of two similar triangles is in the ratio 3:4. The sum of their areas is 75 sq cm. What is the area of the smaller triangle?
• Two triangles are similar and have sides of 8, 12, 28 and 6, 9, 21. What is the ratio of similarity between the two triangles?
• Suppose triangle ABC ~ triangle GHI with scale factor 3:5, and AB=9, BC=18 and AC=21. What is the perimeter of triangle GHI?
• A 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it?
• Use proportions to solve for x on the given triangular composite figure?
• A person is standing 40ft away from a street light that is 30ft tall. How tall is he if his shadow is 10ft long?
• A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is 18 feet above the ground. How many feet long is the shadow of that tree?
• A pizza packages its circular pizzas in a cardboard box. The boxes are formed by folding in 1" squares from the corners of the cardboard. If the volume of the box is 324 cubic inches, what are the dimensions of the box, in inches? Draw it?
• When placed in the box, a large pizza can be described as being "inscribed" in a square box. If the pizza is 1" thick, find the volume of the pizza, in cubic inches given the volume of the box is 324 cubic inches?
• A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?
• Yosief is 4 feet 9 inch boy. He stands in front of a tree and sees that it's shadow coincide with his. Yosief shadow measures 9 feet 6 inches. Yosief measures the distance between him and the tree to calculate its height, how does he do it?
• Given two similar triangles with a scale factor of a : b, show the ratio of their perimeters is also a : b?
• Let #△ABC ~ △XYZ#. The ratio of their perimeters is 11/5, what is their similarity ratio of each the sides? What is the ratio of their areas?
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• The sun casts a shadow of a pine tree on the ground. The tree is 65 feet tall. The angle of depression is 53.4°. What is the length of the shadow?
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• If the ratio of the sides of two similar triangles is 4:9, how do you find the ratio of their areas?
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• Javier (who is exactly 5 feet tall) notices that his shadow is 4 feet long and that the shadow of a nearby tree is 10 feet long. How tall is the tree?
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• If #BE#||#CD#, find #x#?
• What is the value of x?
• Based on the shortest leg of the triangle illustrated, if a similar triangle on the coordinate plane has its shortest leg defined by the points (2, 3) and (8, 3), what is the third point? A) (2, -5) B) (2, -6) C) (2, -7) D) (2, -8)
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