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leonid [27]
3 years ago
15

ABCD is a parallelogram. AE ⊥ DC, A[] ⊥ BC, AD = 10, AB = 15, A[] = 12. Find the length of AE.

Mathematics
1 answer:
kaheart [24]3 years ago
8 0

Answer:

AE= 8

Step-by-step explanation:

The parallelogram forms two right triangles and since it's a parallelogram the opposite angles are congruent meaning you can say the triangles are similar through AA~. The ratio is 2:3 and FA =12 making AE= 8

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Any help would be appreciated. Thank you!
trapecia [35]

Answer:

Area =62.5\sqrt{6} square units

AB=5\sqrt{15} units

BC=5\sqrt{10} units

Step-by-step explanation:

In a right triangle the altitude drawn to the hypotenuse is the geometric mean of the segments at which this altitude divides the hypotenuse.

So,

BD^2=15\cdot 10\\ \\BD^2=150\\ \\BD=\sqrt{150}=5\sqrt{6}\ units

a. The area of the triangle ABC is

A_{ABC}=\dfrac{1}{2}\cdot BD\cdot AC=\dfrac{1}{2}\cdot 5\sqrt{6}\cdot (15+10)=\dfrac{125\sqrt{6}}{2}=62.5\sqrt{6}\ un^2.

b. The legs of the right triangle are geometric means of the segment adjacent to this leg and the hypotenuse, so

AB^2=AD\cdot AC=15\cdot 25\Rightarrow AB=5\sqrt{15}\ units\\ \\BC^2=CD\cdot AC=10\cdot 25\Rightarrow BC=5\sqrt{10}\ units

5 0
3 years ago
Please someone explain this one? Thank you!
den301095 [7]
About 7,460 punds if you add everything together

5 0
3 years ago
Read 2 more answers
the sum of two numbers is 70. the larger number is five less than twice the smaller number . what are the two numbers
earnstyle [38]
X+y=70
x=2y-5
x=larger number
y=smaller number
now plug in the value of x to only have one variable in the equation...
Way to solve for y:
(2y-5)+y=70
3y-5=70
add 5 on both sides...
3y=75
divide by 3 on both sides
y=25
1st way to solve for x:
now plug in y in the original equation...
x+25=70
subtract 25 on both sides...
x=45
2nd way to solve for x:
plug in y for the second equation...
x=25(2)-5
x=50-5
x=45
answer: the two numbers are 45 and 25.

3 0
3 years ago
If ☆ x 2 = 0, then ☆ 8 will equal:<br> 0 + 6<br> O + 8<br> 0 x 2<br> O X4<br> 0 x 8
soldier1979 [14.2K]
The last one I think
3 0
2 years ago
Please help with the question above :)!!! ^^
zhannawk [14.2K]
(-1,-9) because if we substituted 1 into x y would be 9 and if we substituted 1/2 into x y would be 3 but if we substituted -1 into x y would be 1/9 so therefore that value is incorrect

7 0
3 years ago
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