Question

use the chart below for steps 2 - 7. each measurement is written in centimeters. a^{2}+b^{2}=c^{2}
short leg, long leg, hypotenuse square of short leg square of long leg square of hypotenuse
3, 4, ___ 3^{2}=9 4^{2}=16
5, 12, ___
6, 8, ___
8, 15, ___
step 2: measure the length of the hypotenuse of the triangle you drew in step 1. round the measurement to the nearest centimeter. fill in the blank in the first column with this measurement.
step 3: find the square of the hypotenuse. fill in the last column as shown in the middle columns.
step 4: on scratch paper, draw another right triangle with the two legs given in the next row of the table. measure the hypotenuse to the nearest centimeter. complete the row.
step 5: repeat the process for the remaining two right triangles.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\), so \(c = \sqrt{a^{2}+b^{2}}\).

Step2: For the first row (\(a = 3\), \(b = 4\))

\(c=\sqrt{3^{2}+4^{2}}=\sqrt{9 + 16}=\sqrt{25}=5\), and \(c^{2}=25\).

Step3: For the second row (\(a = 5\), \(b = 12\))

\(c=\sqrt{5^{2}+12^{2}}=\sqrt{25+144}=\sqrt{169}=13\), and \(c^{2}=169\).

Step4: For the third row (\(a = 6\), \(b = 8\))

\(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100}=10\), and \(c^{2}=100\).

Step5: For the fourth row (\(a = 8\), \(b = 15\))

\(c=\sqrt{8^{2}+15^{2}}=\sqrt{64+225}=\sqrt{289}=17\), and \(c^{2}=289\).

The completed table is:

Short Leg, Long Leg, Hypotenuse	Square of Short Leg	Square of Long Leg	Square of Hypotenuse
\(5,12,13\)	\(5^{2}=25\)	\(12^{2}=144\)	\(13^{2}=169\)
\(6,8,10\)	\(6^{2}=36\)	\(8^{2}=64\)	\(10^{2}=100\)
\(8,15,17\)	\(8^{2}=64\)	\(15^{2}=225\)	\(17^{2}=289\)

Answer:

Short Leg, Long Leg, Hypotenuse	Square of Short Leg	Square of Long Leg	Square of Hypotenuse
\(5,12,13\)	\(25\)	\(144\)	\(169\)
\(6,8,10\)	\(36\)	\(64\)	\(100\)
\(8,15,17\)	\(64\)	\(225\)	\(289\)