The area of a triangular block is 81 square inches. If the base of the triangle is twice the
height, how long are the base and the height of the triangle?

The base and height of the triangle is 18 inches and 9 inches respectively.

Step-by-step explanation:

Given,

The base of a triangle is twice of the height.

Area = 81 sq inches

Let,

Base (b) = 2x

Height (h) = x

To find its height and base.

Formula

Area of the triangle = bh

According to the problem,

bh = 81

or, ×x×2x = 81

or,

or, x =

or, x = 9

So,

Base = 2×9 inches = 18 inches

Height = 9 inches

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

step-by-step explanation:

this woman was an important writer and propagandist during the american revolution. she was a member of the committee of correspondence (in fact the committee was formed in her home) and was an advisor to many of the revolutionary leaders, including george washington and john adams. who was this revolutionary woman?