The base of a right triangle is 8 cm and hypotenuse is 10 cm. Its area will be :a.40 cm2b.48 cm2c.24 cm2d.80 cm2
Question
The base of a right triangle is 8 cm and hypotenuse is 10 cm. Its area will be :
- a. 40 cm²
- b. 48 cm²
- c. 24 cm²
- d. 80 cm²
Solution
To find the area of a right triangle, we first need to find the height. We know that in a right triangle, the hypotenuse^2 = base^2 + height^2. This is the Pythagorean theorem.
Given that the base (b) is 8 cm and the hypotenuse (c) is 10 cm, we can find the height (a) using the formula:
a = sqrt(c^2 - b^2) a = sqrt((10 cm)^2 - (8 cm)^2) a = sqrt(100 cm^2 - 64 cm^2) a = sqrt(36 cm^2) a = 6 cm
Now that we have the height, we can find the area (A) of the triangle using the formula:
A = 1/2 * base * height A = 1/2 * 8 cm * 6 cm A = 24 cm^2
So, the area of the triangle is 24 cm^2. The correct answer is c. 24 cm^2.
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