Question

Compute the area of a triangle with sides 10 x 10 x 16. The area is equal to ______ square units.

1) 48
2) 96
3) 100
4) 160

Answer 1

The area of a triangle with sides 10, 10, and 16 is computed using the Pythagorean theorem to find the height, which is 6. The formula for the area of a triangle is then used to find the area, which is 48 square units.

Step-by-step explanation:

To compute the area of a triangle with sides 10, 10, and 16, we first need to determine whether the sides provided can form a valid triangle and then find the height. Since two sides are equal, this is an isosceles triangle. We'll use the Pythagorean theorem to calculate the height (h). In an isosceles triangle, the altitude to the base also bisects the base, creating two right triangles with legs of length 8 (half of 16) and h, and a hypotenuse of 10.

The Pythagorean theorem states: a2 + b2 = c2, where a and b are the legs, and c is the hypotenuse. So, h2 + 82 = 102, which simplifies to h2 + 64 = 100. Solving for h, we get h = √(100 - 64) = √36 = 6.

Now we can compute the area using the formula: Area = 1/2 × base × height. Substituting the values in, we get Area = 1/2 × 16 × 6, which equals 48 square units. Therefore, the correct option is 1) 48 square units.