Question: In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the length of each leg is 5 cm?
Options:
12.5 cm²
25 cm²
20 cm²
15 cm²
Correct Answer: 25 cm²
Solution:
Area = 1/2 * base * height = 1/2 * 5 * 5 = 12.5 cm².
In a triangle, if one angle is 90 degrees and the other two angles are 45 degree
Practice Questions
Q1
In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the length of each leg is 5 cm?
12.5 cm²
25 cm²
20 cm²
15 cm²
Questions & Step-by-Step Solutions
In a triangle, if one angle is 90 degrees and the other two angles are 45 degrees each, what is the area if the length of each leg is 5 cm?
Step 1: Identify the type of triangle. This triangle has one angle of 90 degrees and two angles of 45 degrees, making it a right-angled isosceles triangle.
Step 2: Understand the sides of the triangle. In a right-angled isosceles triangle, the two legs (the sides that form the right angle) are equal in length. Here, each leg is 5 cm.
Step 3: Use the formula for the area of a triangle. The area of a triangle is calculated using the formula: Area = 1/2 * base * height.
Step 4: Identify the base and height. In this triangle, both the base and height are the lengths of the legs, which are both 5 cm.
Step 5: Substitute the values into the area formula. Area = 1/2 * 5 cm * 5 cm.
Step 6: Calculate the area. Area = 1/2 * 25 cm² = 12.5 cm².
Triangle Properties – Understanding the properties of a right triangle, specifically the angles and the relationship between the legs.
Area Calculation – Applying the formula for the area of a triangle using the base and height.
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