This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here are the calculations for the values of x and y: a) The two triangles are similar, meaning their corresponding sides are proportional. The sides of the smaller triangle are 5 m, 7 m, and x. The sides of the larger triangle are 10 m, 14 m, and 16 m. Step 1: Set up the proportion of corresponding sides. We can see that 5 m corresponds to 10 m (since (5)/(10) = (1)/(2)) and 7 m corresponds to 14 m (since (7)/(14) = (1)/(2)). Therefore, x must correspond to 16 m. (5)/(10) = (x)/(16) Step 2: Solve for x. Simplify the ratio: (1)/(2) = (x)/(16) Multiply both sides by 16: x = (16)/(2) x = 8 The value of x is 8 m. b) The two triangles are similar. The sides of the smaller triangle are 3 cm, 3 cm, and y. The sides of the larger triangle are 9 cm, 9 cm, and 5 cm. Step 1: Set up the proportion of corresponding sides. Since both triangles appear to be isosceles, the equal sides of the smaller triangle (3 cm) correspond to the equal sides of the larger triangle (9 cm). The ratio of similarity is (3)/(9) = (1)/(3). Therefore, the third side of the smaller triangle (y) must correspond to the third side of the larger triangle (5 cm). (3)/(9) = (y)/(5) Step 2: Solve for y. Simplify the ratio: (1)/(3) = (y)/(5) Multiply both sides by 5: y = (5)/(3) The value of y is (5)/(3) cm. That's 2 down. 3 left today — send the next one.