Find the legnth of a side of a square if its area is the same as the area of a triengle with an altitude of 18 cm and a base of 11cm.
2007-04-12 10:01:40 · 11 answers · asked by Sarah 1 in Science & Mathematics ➔ Mathematics
Area of a triangle formula
A = 1/2 b h
A = 1/2 (11)(18)
A = 1/2(198)
A = 198/2
A = 99 cm
x² = 99
√x² = ± √99
x = ± 9.949874371 cm
x = ± 9.95 cm
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2007-04-12 10:58:52 · answer #1 · answered by SAMUEL D 7 · 0⤊ 0⤋
Area of square = Area of the traingle
Let us suppose 'a' be the side of the square then
Area of square = side of the square * side of the square = a * a.
Now Area of triangle = 1/2 * Base * Height(Altitude)
Therefore,
a * a = 1/2 * 11 * 18
a * a = 11 * 9
a = Square root of ( 11 * 9)
therefore the side of the square , a = 3*(square root of 11) cm
2007-04-12 10:09:28 · answer #2 · answered by Anand 2 · 0⤊ 0⤋
ok, we have the square. Let's say each side is x. The area of this square is therefore x^2, or x squared.
The triangle's altitude is also its height, and they gave us the base. To find the area of this triangle, we'd do 18 * 11 = 198. THen, 198/2 = 99.
The areas are the same, right? That means that x^2 = 99. X, or the length of one side of the square, would be the square root of 99
Hope this helped ^__^
2007-04-12 10:07:53 · answer #3 · answered by Lynne L 2 · 0⤊ 0⤋
The area of the triangle is equal too:
(1/2) * base * hieght = (1/2) * 11 * 18 = 99 cm
The area of a square is equal to the length of its side squared:
side ^ 2 = Area = 99
to find the length of the side take the square root of both sides and you get:
side = sqroot(99) = 3 * sqroot(11) = 9.94987 cm
2007-04-12 10:11:16 · answer #4 · answered by bartathalon 3 · 0⤊ 0⤋
Area of triangle
Base x Height / 2
18cm x 11cm = 198cm
198cm / 2 = 99cm
square root of 99cm = 9.95cm
so the length of a square is 9.95 cm
=)
2007-04-12 10:05:46 · answer #5 · answered by cutie.pie_xo 3 · 0⤊ 0⤋
area of a square is side * side
area of a triangle is base * altitude * 1/2
so, the area of this triangle is 18 * 11 * 1/2 = 99
so, to find a side of the square we can do this equation
x^2 = 99
and taking the square root of both sides, we get
3sqrt(11), which is approximately 9.95
2007-04-12 10:06:17 · answer #6 · answered by Anthony T 3 · 0⤊ 0⤋
Area of triangle = 1/2 base times height
A = (1/2)(18)(11) = 99
we want ti to have the same area
Area of square is side times side
A = x^2
x^2 = 99
x = sqrt(99) which simplifies to 3sqrt(11)
:)
each side will be 3sqrt(11)
2007-04-12 10:05:45 · answer #7 · answered by MathMark 3 · 0⤊ 0⤋
Area of Triangle= 1/2base x height
11/2 x 18 = 135 cm.
A square is only a square if all 4 sides are equal length.
Area of Square= length x width, so if all sides same length, then the length and width are the same, so ....
135 cm/2 sides=67.5 cm is your square side length.
2007-04-12 10:10:51 · answer #8 · answered by clevelandbrownsgirl2007 3 · 0⤊ 1⤋
as a manner to ingredient you are able to desire to locate a variety it is a diverse of all 3 phrases. For this concern that variety is 10. you are able to rewrite your equation as: 10*(2m + 3n - a million)
2016-10-21 23:50:29 · answer #9 · answered by ? 4 · 0⤊ 0⤋
the square root of 99...now go finish your homework
2007-04-12 10:05:20 · answer #10 · answered by Anonymous · 0⤊ 0⤋