Question

The lengths of the sides of a right triangle are a and b, and the hypotenuse is c. Find the area of the triangle. b = 2 in.; c = 6 in. A = sq. in.

Answer 1

`a = √(32)\text{ inch}`

Rea of triangle =
`A = √(32)\text{ square inches}`

Explanation:

We are given the following information:

The lengths of the sides of a right angled triangle are a and b, and the hypotenuse is c.

b = 2 inch

c = 6 inch

We have to find the area of the triangle.

Since, the given triangle is a right angles triangle, it satisfies the Pythagoras theorem.

The Pythagoras statement states that:

• In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides.

Thus,

`a^2 + b^2 = c^2\\\text{Putting all the values}\\a^2 + (2)^2 = (6)^2\\a^2 = 36 -4 = 32\\a = √(32)\text{ inch}`

Area of triangle =

`\displaystyle(1)/(2)* \text{Base} * \text{Height}\\\\= (1)/(2)* a * b\\\\=(1)/(2)* 2* √(32)\\=√(32)\text{ square inches}`

Answer 2

`√(32)sq. in`

Explanation:

To find the area of a triangle, we need to know the base and perpendicular to the base (height) of the triangle.

For a right triangle,

(Hypotenuse)² = (Base)² + (Perpendicular)²

We can find the perpendicular first from the above relation.

Given, Hypotenuse, c = 6 in

Base, b = 2 in

Perpendicular,
`a = √(c^2-b^2) = \sqrt {6^2-2^2}=√(36-4)=√(32)`

The area of triangle:

`A = (1)/(2){b}{a} = (1)/(2)* 2 * √(32) =√(32)sq. in.`