In triangle ABC, ab = 17, AC = 15, the center line ad on the side of BC = 4, calculate the area of triangle ABC

Extend ad to point e so that de = ad, connect be, CE
Then ABEC is a parallelogram
∴BE=AC=15
∵AD=4
∴AE=8
∵8 ²+ fifteen ²= seventeen ²
∴∠AEB=90°
Area of parallelogram ABEC = 15 * 8 = 120
△ area of ABC = 60

In triangle ABC, ab = 10, AC = 17, height ad = 8, what is the length of BC My answer is also 21, but the teacher approved one and a half pairs. Are there two answers?

According to Pythagorean theorem, CD = 15, BD = 6
When D is on BC, BC = 15 + 6 = 21
When D is on the extension line of BC, BC = 15-6 = 9

In RT triangle ABC, angle c = 90 degrees, AC = 4, BC = 2, D is the midpoint of BC, then (vector AB vector AC) × Vector ad =? If e is the midpoint of AB and P is any point of triangle ABC (including boundary), then vector ad × What is the value range of vector EP?

∵ in RT △ ABC, ∠ C = 90 °, AC = 4, BC = 2, D is the midpoint of BC, then
^AD ²= (^AB ²+^ AC ²)/ 2,
^AB ²=^ AC ²+^ BC ²= 16+4=20．
∴(^AB-^AC)·^AD=(^AB-^AC)·(^AB+^AC)/2 =(^AB ²-^ AC ²)/ 2=(20-16)/2=2．
Establish a plane rectangular coordinate system with the straight line where CA is located as the X axis and the straight line where CB is located as the Y axis, so that the coordinates of a are (4,0) and B are (0,2),
According to the midpoint formula of the line segment, the coordinates of point D are (0,1), the coordinates of point e are (2,1), and the coordinates of point P are (x, y),
From the meaning of the question, we can get that the feasible area is △ ABC and its internal area, so there are
x≥0
y≥0
x/4+y/2≤1
．
Let t = ^ ad · ^ EP = (- 4,1) · (X-2, Y-1) = 7-4x + y, that is, y = 4x + T-7
Therefore, when the straight line y = 4x + T-7 passes through point a (4,0), the minimum value of T is 7-16 + 0 = - 9,
When the straight line y = 4x + T-7 passes through point B (0,2), the maximum value of T is 7-0 + 2 = 9,
Therefore, the value range of T = ^ ad · ^ EP is [- 9,9]
Use this symbol to represent ^ vector

In triangle ABC, ab = 7, BC = 5, AC = 6, what is the value of vector AB into vector BC

AB = 7, BC = 5, AC = 6, so CoSb = (AB ^ 2 + BC ^ 2-ac ^ 2) / 2 * AB * BC = (7 ^ 2 + 5 ^ 2-6 ^ 2) / 2 * 7 * 5 = 19 / 35, then AB * BC = | ab| * | bc| * cos (π - b) = 7 * 5 * (- 19 / 35) = - 19. I'm glad to answer for you! If you are satisfied with my answer, please click the "adopt as satisfactory answer" button below. If there are other

If the perimeter of a right triangle is 24 and the length of the hypotenuse is 10, its area is () A. 96 B. 49 C. 24 D. 48

If the perimeter of a right triangle is 24 and the length of the hypotenuse is 10, the sum of the two right sides is 24-10 = 14,
If one right angle side is x, the other side is 14-x,
According to Pythagorean theorem, X2 + (14-x) 2 = 100,
The solution is x = 6 or 8,
So the area is 6 × 8÷2=24．
Therefore, C

In triangle ABC, ab = 17, AC = 15, the center line ad on the side of BC = 4, calculate the area of triangle ABC