Two sides of a right triangle measure 222 units and 444 units.
2\text{ units}2 units4\text{ units}4 units
What is the area of the square that shares a side with the third side of the triangle?
Answers
Given : Two sides of a right triangle measure 2 units and 4 units.
To Find : area of the square that shares a side with the third side of the triangle
Solution:
Case 1 : If Two sides of a right triangle measure 2 units and 4 units.
if sides are perpendicular sides
Then using Pythagorean theorem
third side² = 2² + 4²
=> third side² = 4 + 16
=> third side² = 20
area of the square that shares a side with the third side of the triangle = third side² = 20 sq units
Case 2 : If 4 units is hypotenuse side
Then using Pythagorean theorem
third side² = 4² - 2²
=> third side² = 16 - 4
=> third side² = 12
area of the square that shares a side with the third side of the triangle = third side² = 12 sq units
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Answer:
20 units^2
Step-by-step explanation:
We can use the Pythagorean theorem to find the area of the square for the third side.
The equation for the Pythagorean theorem is
a^2 + b^2 = c^2a
2
+b
2
=c
2
a, squared, plus, b, squared, equals, c, squared
where aaa and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.
Hint #22 / 3
In this case, a = 2, b = 4a=2,b=4a, equals, 2, comma, b, equals, 4, and c = xc=xc, equals, x.
\begin{aligned} a^2 + b^2 &= c^2 \\\\ 2^2 +4^2&= \blueD{ x^2}\\\\ 4 + 16 & =\blueD{ x^2} \\\\ \blueD{20} & = \blueD{x^2} \\\\ \end{aligned}
a
2
+b
2
2
2
+4
2
4+16
20
=c
2
=x
2
=x
2
=x
2
The area of the square for the third side of the triangle is 20 units^2
squared.