Respuesta :
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 = [tex]\frac{x}{2}[/tex]
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;
[tex](x)^2+(\frac{x}{2}) ^2 = 125^2\\\\x^2+\frac{x^2}{4}=15625[/tex]
Now taking LCM to make the denominator we get;
[tex]\frac{4x^2}{4}+\frac{x^2}{4}=15625\\\\\frac{4x^2+x^2}4=15625\\\\\frac{5x^2}{4}=15625\\[/tex]
Now Multiplying both side by [tex]\frac{4}{5}[/tex] we get;
[tex]\frac{5x^2}{4}\times\frac{4}{5}=15625\times \frac{4}{5}\\\\x^2= 12500[/tex]
Taking square root on both side we get;
[tex]\sqrt{x^2}= \sqrt{12500}\\ \\x= 111.80 \approx 112\ mm[/tex]
Length of longer leg = 112 mm
Length of shorter leg = [tex]\frac{x}{2}= \frac{112}{2} = 56\ mm[/tex]
Hence best approximates the lengths of the legs of a right angled triangle 112 mm and 56 mm.
