You found CD from the Pythagorean theorem to be ...
... CD = √(5² -2²) = √21
Since triangle ADC ~ triangle ACB, the ratios of corresponding sides are the same:
... AC/AD = AB/AC
... AB = AC²/AD
... AB = 5²/2 = 12.5 . . . . . . . the base of the overall triangle
_____
Then the area (A) is ...
... A = (1/2)bh
... A = (1/2)(12.5)(√21) ≈ 28.64 square units
_____
As you see here, the altitude of a right triangle divides it into three similar triangles. From smallest to largest, they are ...
... ADC ~ CDB ~ ACB
You can figure this using AAA similarity, since the smallest and largest triangles listed above share an acute angle vertex (∠A). That, together with the right angle, means all angles are congruent. After that, then you know ∠ACD ≅ ∠CBD, so you can show the middle sized triangle is similar to the other two.
Answer:
28, 32, 36
Step-by-step explanation:
If you multiply each 7, 8, and 9 by 4 you get 28, 32, and 36. The sum of those numbers is 96.
To avoid multiplying the two numbers and then finding the cube root, find the cube root of each number first. the cube root of 27 is 3x3x3, so you can take out the three to outside of the sqrt, to get 3 cube root 18. eighteen does not have a cube root, so that's all you have to do. the answer would be 3 (cube root) 18.
Answer:
-88x + 10y
Step-by-step explanation:
-5x+3y= -93x+7y=23
we cannot do anything to numbers with unlike signs so we will do this
23=-5x+3y=-93x+7y
now we will take the numbers with like signs to one place like this
23=-5x+93x+3y+7y
now we can solve this
- x + = -
+ x+=+
-x-=-
23= 88x+10y ANSWER