Question is Incomplete; Complete question is given below;
Which best approximates the lengths of the legs of a right triangle if the hypotenuse is 125 mm and the shorter leg is one-half the length of the longer leg?
A. 25 mm and 55 mm.
B. 56 mm and 112 mm.
C. 5 mm and 10 mm.
D. 63 mm and 63 mm.
Answer:
B. 56 mm and 112 mm.
Step-by-step explanation:
Given:
Length of the hypotenuse = 125 mm
the shorter leg is one-half the length of the longer leg.
Let the length of the longer leg be 'x'.
So the length of the shorter leg = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
we need to find the shorter and longer lengths of the triangle.
Solution:
Since it is given that the triangle is right angled triangle.
Then by using Pythagoras theorem which states that;
"The sum of the square of the the lengths of the legs of a right angle triangle is equal to square of its hypotenuse."
Framing in equation form we get;
![(x)^2+(\frac{x}{2}) ^2 = 125^2\\\\x^2+\frac{x^2}{4}=15625](https://tex.z-dn.net/?f=%28x%29%5E2%2B%28%5Cfrac%7Bx%7D%7B2%7D%29%20%5E2%20%3D%20125%5E2%5C%5C%5C%5Cx%5E2%2B%5Cfrac%7Bx%5E2%7D%7B4%7D%3D15625)
Now taking LCM to make the denominator we get;
![\frac{4x^2}{4}+\frac{x^2}{4}=15625\\\\\frac{4x^2+x^2}4=15625\\\\\frac{5x^2}{4}=15625\\](https://tex.z-dn.net/?f=%5Cfrac%7B4x%5E2%7D%7B4%7D%2B%5Cfrac%7Bx%5E2%7D%7B4%7D%3D15625%5C%5C%5C%5C%5Cfrac%7B4x%5E2%2Bx%5E2%7D4%3D15625%5C%5C%5C%5C%5Cfrac%7B5x%5E2%7D%7B4%7D%3D15625%5C%5C)
Now Multiplying both side by
we get;
![\frac{5x^2}{4}\times\frac{4}{5}=15625\times \frac{4}{5}\\\\x^2= 12500](https://tex.z-dn.net/?f=%5Cfrac%7B5x%5E2%7D%7B4%7D%5Ctimes%5Cfrac%7B4%7D%7B5%7D%3D15625%5Ctimes%20%5Cfrac%7B4%7D%7B5%7D%5C%5C%5C%5Cx%5E2%3D%2012500)
Taking square root on both side we get;
![\sqrt{x^2}= \sqrt{12500}\\ \\x= 111.80 \approx 112\ mm](https://tex.z-dn.net/?f=%5Csqrt%7Bx%5E2%7D%3D%20%5Csqrt%7B12500%7D%5C%5C%20%5C%5Cx%3D%20111.80%20%5Capprox%20112%5C%20mm)
Length of longer leg = 112 mm
Length of shorter leg = ![\frac{x}{2}= \frac{112}{2} = 56\ mm](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%3D%20%5Cfrac%7B112%7D%7B2%7D%20%3D%2056%5C%20mm)
Hence best approximates the lengths of the legs of a right angled triangle 112 mm and 56 mm.