Hi!
This is a fun one, as it delves into basic trigonometry.
We're going to use the Pythagorean theorem here, which says that for right triangles where "c" is the hypotenuse,
a² + b² = c²
We have to split this large triangle into two parts, both of which are right triangles. (This is why they drew a line in the middle to tell you that the larger triangle is composed of two right triangles.)
Let's do the one on the right first.
We know that the length of the hypotenuse is 10, and that the length of one of the legs is 6.5. If we plug this into our equation, we'll get the length of the other leg. I'm choosing "b" to be 6.5, but it really doesn't matter if you pick "a" or "b", so long as you reserve "c" for the hypotenuse (longest side).
a² + 6.5² = 10²
a² + 42.25 = 100
a² = 57.75
√a² = √57.75
a ≈ 7.6
Therefore, the length of DC is about 7.6.
Find the length of AD using the same method (7.5 is the hypotenuse "c", and 6.5 is one of the legs "a" or "b"). Then, once you have AD, add the lengths of AD and DC to get AC.
Have a great one!
We have 2 different equations with which we need to work to find the answer to this. First off, the area formula is A = L * W. Our area is 12, so 12 = L * W. Then we have the Pythagorean's theorem we have to worry about, which says that . We are going to solve the area equation for L to get . What we are going to do now is sub that into the other formula in place of L to get and . In order to solve for w, we need to multiply all those terms by w^2 to get rid of the denominator. That leaves us with this then: . We need to factor that now to solve for w. We will bring everything over to the one side of the equation and set it equal to 0. . We are going to use a u substitution here to make the factoring easier. We are going to let so . Now we will factor . When we factor that we get (u - 16)(u - 9). By the Zero Product Property, either u - 16 = 0 or u - 9 = 0. u = 16 and u = 9. But remember that u = w^2, so what we really have, after we make the replacement, is so w = 4, and and w = 3. Now it just so happens that if the length is 4 and the width is 3, the product of those is 12 (the area), and if you remember, in a right triangle with a hypotenuse of 5, the side lengths will be 3 and 4. So your dimensions of the rectangle are that the length is 4 and the width is 3. There you go!
Answer:
166.1? this is how i would do it
Step-by-step explanation:
A. 4x4x6= 96
B. 3.5x3.5x2= 24.5
C. 3.8x3x4= 45.6
96+24.6+45.6= 166.1
Answer:
10:35
Step-by-step explanation: