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If it's a right angle triangle then use Pythagoras' theorem to find the 3rd side

Q: What is the length of altitude drawn to the hypotenuse of a triangle with given sides of 7 and 21?

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A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base? WRONG WRONG WRONG NO NO NO ::"::":""::":"""::"":":""::::::::::::: ::"::": ::":: :: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::"

To find the length of a line drawn between 2 vertices which are not next to each other, first draw a right triangle such that the line is the hypotenuse and the other two lines are drawn parallel to the x-axis and y-axis. Since the length of the other two lines are known, you can then calculate the hypotenuse to find the length of the line between the two vertices.

Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle. Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from a vertex to the opposite side and is perpendicular with that opposite side, it can only occur if it is outside the triangle. Look at the triangle in related links. If you look at the vertex on the top, the only way to draw the altitude would be to draw outside the triangle.

The rectangle has an area of 12 x 8 = 96 square inches. The triangle has an area of (1/2 * 32 * x). So, 16x = 96, therefore x = 6. The height of the triangle is 6 inches.

The altitude will be 6 inches in length. The area of the rectangle is length (l) times width (w) or l x w = 12 x 8 = 96 The area of a triangle is 1/2 the base (b) times the height (h), or altitude, and, because the area of the triangle is equal to the area of the rectangle, both will have an area of 96. For the triangle, 1/2 b x h = 1/2 x 32 x h = 96, and 16 x h = 96, and h = 6

Related questions

There is not enough information for an unambiguous answer. If the missing side is the hypotenuse, then the altitude is 4.910 units. If the missing sides is one of the legs of the triangle, the altitude is 4.907 units.

A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base?

If a remains the right triangle, No

The length of the circle's diameter

6

A rectangle and a triangle have equal areas. The length of the rectangle is 12 inches, and its width is 8 inches. If the base of the triangle is 32 inches, what is the length, in inches, of the altitude drawn to the base? WRONG WRONG WRONG NO NO NO ::"::":""::":"""::"":":""::::::::::::: ::"::": ::":: :: ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::"

Its diameter.

To find the length of a line drawn between 2 vertices which are not next to each other, first draw a right triangle such that the line is the hypotenuse and the other two lines are drawn parallel to the x-axis and y-axis. Since the length of the other two lines are known, you can then calculate the hypotenuse to find the length of the line between the two vertices.

Draw the isosceles trapezoid ABCE, where the length of the bases AB (on the top) and EC are respectively 10 and 20. From A and B draw the perpendiculars to the base EC of the trapezoid, and label the point of intersections with F and G). The rectangle ABGF is formed, where the length of FG is 10 (since the two opposite sides of a rectangle are congruent). Then the lengths of EF and GC are 5 (since the trapezoid is isosceles). Draw the diagonal AC. From C and E draw the parallel lines respectively to AE and AC, and label the intersection point with D. So the rectangle ACDE is formed. Thus, the triangle EAC is a right triangle, where the angle A is 90 degrees (as the angle of a rectangle), and AF is the altitude drawn at the hypotenuse EC. We have a theorem that states: "If an altitude is drawn to the hypotenuse of a right triangle, then each leg is the geometric mean between the hypotenuse and its touching segment on the hypotenuse". So we have, EC/AE = AE/EF, which yields AE2 = EC*EF, and so AE = √(20*5) = 10. or using the same diagram, Since the diagonals of a rectangle bisect each other (let's say they bisect at H), then AH is the median of the right triangle EAC, drawn to the hypotenuse EC, so its length is the half of the hypotenuse. So the length of AH is 10. Since the trapezoid is isosceles, then the diagonal BE also will form a right triangle EBC, where the median BH also it is 10. So the triangle ABH is equilateral, where angle A is 60 degrees, and it is congruent with angle H of the triangle AHE, as two alternate interior angles. Thus, the isosceles triangle AHE is also equilateral, where AE = 10.

An isosceles triangle is usually drawn with the two sides of equal length as the legs and the third side as the base. For a right angled isosceles triangle then the hypotenuse is drawn as the base with the two sides of equal length as the legs joining together at a right angle. Draw a circle. Draw a horizontal diameter with a second diameter perpendicular to the first. The hypotenuse is the horizontal diameter. Draw lines from the ends of this diameter to the point where one end of the second diameter meets the circumference. These are the two equal legs of the isosceles triangle. These legs meet at an angle of 90° .

An altitude is a perpendicular drawn from a point to the opposite segment while a median is a segment drawn from a point to the opposite side such that it bisects the side.Altitudes and their concurrenceMedians and their concurrence

To construct a right triangle given the radius of the circumscribed circle and the length of a leg, begin with two ideas. First, the diameter of the circle is equal to twice the radius. That's pretty easy. Second, the diameter of the circle is the length of the hypotenuse. The latter is a key to construction. Draw your circle, and draw in a diameter, which is the hypotenuse of the right triangle, as was stated. Now set you compass for the length of the leg of the triangle. With this set, place the point of the compass on one end of the diameter (the hypotenuse of your triangle), and draw an arc through the circumference of the circle. The point on the curve of the circle where the arc intersects it will be a vertex of your right triangle. All that remains is to add the two legs or sides of the triangle. Draw in line segments from each end of the hypotenuse (that diameter) to the point where your arc intersected the curve of the circle. You've constructed your right triangle. Note that any pair of lines that is drawn from the ends of the diameter of a circle to a point on the curve of the circle will create a right triangle.