Is the area of a 45-45-90 triangle with leg length of 2 inches is the same as the area of a square with leg?

Question

length square 2 inches? I said this is false is that right.

Answer 1

Picture a right triangle:
It has the length of a leg of 2.

A square formed with one side being that leg, will have double the area.

Here is more information on what is the leg of a triangle:
http://www.mathwords.com/l/leg_of_right_triangle.htm

You are correct. The answer is false. Draw a picture when you do geometry problems. It will help you to visualize and understand what the problem is asking.

Answer 2

Yes, and here's the reasoning.

Since the triangle is 45-45-90, the height will be equal to the distance from each end of the base line to the point below the apex (necessarily the mid-point of the base).

As the area of a triangle = 1/2 x base x height, and here the base = twice the height, the area is exactly the square of the height.

I hope this helps, but do please feel free to drop me a line if you'd like me to go over this or any other figure-work in further detail.

Answer 3

The area of a triangle is (1/2) * base * height.

Your triangle is a special right triangle, 45deg-45deg-90deg, so the leg lengths are equal.
The legs are your base and height measurements, and are 2 in. each.

The area of this triangle is (1/2) * leg * leg.

The area of the triangle is:
(1/2) * 2 in. * 2 in. =
(1/2) * 4 sq.in. =
2 sq. in.

The area of a square is base * height.

For the square, the leg length is the base and the height. The leg length is 2 in.

The area of the square is leg * leg.

the area of the square is:
2 in. * 2 in. =
4 sq. in.

Is the area of the triangle the same as the area of the square?
(1/2) * leg * leg ?= leg * leg
(1/2) * leg^2 != leg^2
2 sq. in. ?= 4 sq. in
2 sq. in. != 4 sq. in.
no, the areas are not equal.

(If you draw this out: draw a square with edges of 2 in. (A square has all 4 legs equal in length, all corners are 90 deg.) Now cut it like a sandwich corner to corner. (The angles at the cut are cut in half, are now 45deg.) This creates two 45-45-90 triangles inside the square with leg lengths of the same 2 in. as the square. Since you are finding the area of one triangle as compared to the square, the square is 2 times as big as the triangle, since you can fit 2 triangles inside of the square.)

you are correct in answering false.

Answer 4

the area of the triangle is l^2/2 This triangle is isocele with length
2 . So its area is 2*2/2=2inch^2

while a square of length 2inches has an area of 2*2 = 4 inch ^2

so you were right

Answer 5

of course you're right!!!!! congrats!!!

that is because the formula for the area of the triangle is

A = 1/2bh

while the square's formula for its area:

A = bh

and even if the have the same length of the legs,,,they still don't have the same area...

Answer 6

If I unerstand you, the statement true
The area of the triangle is 2*2/2 = 2 in^2
The area of a square with side = sqrt(2) is (sqrt(2))^2 = 2in^2.

Thye are the same.

Answer 7

triangle area = (1/2)(2)(2)=2

square area = (SQRT2)(SQRT2) = 2

Answer 8

u r right mate