McGraw Hill Glencoe Geometry, 2012
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McGraw Hill Glencoe Geometry, 2012 View details
6. Two-Dimensional Figures
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Exercise 40 Page 63

Find the hypotenuse using the Pythagorean Theorem.

Perimeter: ≈ 3.4in
Area: ≈ 0.5in^2

Practice makes perfect

We can use the values shown on the given diagram to calculate the perimeter and area of the triangle.

Finding the Perimeter

To find the perimeter, we need the length of all three sides of this right triangle. From the figure, we know that two segments are marked with one hatch mark. Therefore, both of them have the same length. Additionally, we know that 2.5cm is approximately equal to 1inch, so we can convert the side lengths into inches right away.

Next, we can use the Pythagorean Theorem to find the length of the hypotenuse.
a^2+b^2=c^2
1^2+ 1^2≈ c^2
Simplify
1+1≈ c^2
2≈ c^2
sqrt(2)≈ c
c≈ sqrt(2)
c≈ 1.4
The hypotenuse is approximately 1.4 inches long. Now we can add all of the side lengths to find the perimeter. 1+1+sqrt(2) ≈ 3.4in

Finding the Area

In a right triangle, we can think of one leg as the base and the other leg as the height. Using these values, we can find the area using the formula for area of a triangle.
A=1/2bh
A≈1/2( 1)( 1)
A≈1/2
A≈ 0.5
The area of the triangle is approximately 0.5 square inches.