Question

Which beat 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

Answer 1

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.

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 =
`(x)/(2)`

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+((x)/(2)) ^2 = 125^2\\\\x^2+(x^2)/(4)=15625`

Now taking LCM to make the denominator we get;

`(4x^2)/(4)+(x^2)/(4)=15625\\\\\frac{4x^2+x^2}4=15625\\\\(5x^2)/(4)=15625\\`

Now Multiplying both side by
`(4)/(5)` we get;

`(5x^2)/(4)*(4)/(5)=15625* (4)/(5)\\\\x^2= 12500`

Taking square root on both side we get;

`√(x^2)= √(12500)\\ \\x= 111.80 \approx 112\ mm`

Length of longer leg = 112 mm

Length of shorter leg =
`(x)/(2)= (112)/(2) = 56\ mm`

Hence best approximates the lengths of the legs of a right angled triangle 112 mm and 56 mm.