Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, an
Practice Questions
Q1
Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?
40 cm²
20 cm²
30 cm²
50 cm²
Questions & Step-by-Step Solutions
Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the area of the second triangle if its longest side is 10 cm?
Step 1: Identify the sides of the first triangle, which are 3 cm, 4 cm, and 5 cm.
Step 2: Determine the longest side of the first triangle, which is 5 cm.
Step 3: Identify the longest side of the second triangle, which is given as 10 cm.
Step 4: Calculate the ratio of the longest sides of the two triangles: 10 cm (second triangle) / 5 cm (first triangle) = 2.
Step 5: Since the triangles are similar, the ratio of their areas is the square of the ratio of their sides. So, area ratio = (2)² = 4.
Step 6: Calculate the area of the first triangle using the formula for the area of a triangle. The area of the first triangle is 6 cm².
Step 7: Multiply the area of the first triangle by the area ratio to find the area of the second triangle: 6 cm² * 4 = 24 cm².
