Question

The area of a triangular block is 64 square inches. If the base of the triangle is twice the height, how long are the base and height of the triangle?

Answer 1

Area of the triangle(A) is given by:

`A = (1)/(2)bh` ....[1]

where,

b is the base and h is the height of the triangle.

As per the statement:

The area of a triangular block is 64 square inches.

⇒
`A= 64 in^2`

It is given that: If the base of the triangle is twice the height

⇒
`b = 2h` .....[2]

Substitute these in [1] we have;

`64 = (1)/(2) \cdot (2h) \cdot h`

⇒
`64 = h^2`

or

`h^2 = 64`

⇒
`h = √(64) = 8` inches.

Substitute h =8 in [2] we have;

`b = 2(8) = 16` in.

therefore, the base and height of the triangle are: 16 inches and 8 inches.