1. Rectangle ABCD is shown. What is the length of diagonal AC? Round to the nearest tenth, if necessary.
A_____________B
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8 m |
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D_____13 m____C
A. 10 meters
B. 10.2 meters**
C. 15 meters
D. 15.3 meters
I don't really know how to solve this one and need help!
C^2 = 8^2 + 13^2
C^2 = 64 + 169
C^2 = 233
Square root of 233 would be 15.3!
But you have a right triangle : )
Use the Pythagorean Theorem
C^2 = 8^2 + 13^2
and C is the length of your diagonal : )
And, I was trying to make a square with the lines but that didn't work. The 8 m is on the left side of the square and the 13 m is on the bottom!
It's Helpful
Well, let's take a stroll down Geometry Lane! To find the length of diagonal AC, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, AB and CD are the other two sides of the triangle, and AC is the hypotenuse. So, we can set up our equation as follows:
AB² + CD² = AC²
Given that AB is 8 meters and CD is 13 meters, we can substitute those values into the equation:
8² + 13² = AC²
Simplifying,
64 + 169 = AC²
233 = AC²
Now, we just need to find the square root of 233 to get AC:
AC ≈ √233
And after crunching some numbers, the approximate length of AC comes out to be around 15.264 meters. Since we need to round to the nearest tenth, the answer would be 15.3 meters.
So, D. 15.3 meters is the closest option to our calculated value.
To find the length of diagonal AC, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In the given rectangle, AC is the hypotenuse of a right triangle with sides AD and CD. To apply the Pythagorean theorem, we need to calculate the lengths of AD and CD.
AD is the vertical side of the rectangle, with a length of 8 m.
CD is the horizontal side of the rectangle, with a length of 13 m.
Now, we can calculate the length of AC using the Pythagorean theorem:
AC^2 = AD^2 + CD^2
AC^2 = 8^2 + 13^2
AC^2 = 64 + 169
AC^2 = 233
To find AC, take the square root of both sides:
AC = √233
Rounding to the nearest tenth, we get:
AC ≈ 15.26
Therefore, the length of diagonal AC is approximately 15.3 meters.
The correct answer is D. 15.3 meters.