Question

The pythagorean theorem and maps answer key

Answer 1

I can help u with one question,rest u can do it.
Pythagorean theorem is (hy)^2=(l)^2+(b)^2
Hypotenuse is the lingest side of a triangle

Answer 2

Answer with explanation:

According to Pythagorean Theorem if in a right triangle the two legs of a right triangle are a and b and the hypotenuse is denoted by c then we have:

          $c^2=a^2+b^2$

Ques 1)

By Pythagorean Theorem we have:

                 $(440)^2=(305)^2+a^2\\\\i.e.\\\\193600=93025+a^2\\\\\\a^2=193600-93025\\\\\\a^2=100575\\\\\\a=317.1356\ units$

To the nearest tenth we have:   a=317.1

Ques 2)

By Pythagorean Theorem we have:

                 $(415)^2=(390)^2+b^2\\\\i.e.\\\\172225=152100+b^2\\\\\\b^2=172225-152100\\\\\\b^2=20125\\\\\\b=141.8626\ units$

To the nearest tenth we have:   b=141.9

Ques 3)

By Pythagorean Theorem we have:

$c^2=(625)^2+(450)^2\\\\\\c^2=593125\\\\\\c=770.1460$

To the nearest tenth we have:   c=770.1

Ques 4)

By Pythagorean Theorem we have:

$(515)^2=(380)^2+d^2\\\\\\d^2=120825\\\\\\d=347.5989$

To the nearest tenth we have:   d=347.6

Ques 5)

By Pythagorean Theorem we have:

$(700)^2=(400)^2+e^2\\\\\\e^2=330000\\\\\\e=574.4562$

To the nearest tenth we have:  e=574.4

Ques 6)

By Pythagorean Theorem we have:

$(750)^2=(500)^2+f^2\\\\\\f^2=312500\\\\\\f=559.0169$

To the nearest tenth we have:   f=559

Ques 7)

By Pythagorean Theorem we have:

$(g)^2=(250)^2+(250)^2\\\\\\g^2=125000\\\\\\g=353.5533$

To the nearest tenth we have:   g=353.6

Ques 8)

By Pythagorean Theorem we have:

$(400)^2=(325)^2+h^2\\\\\\h^2=54375\\\\\\h=233.1844$

To the nearest tenth we have:   h=233.2

Ques 9)

By Pythagorean Theorem we have:

$(i)^2=(300)^2+(400)^2\\\\\\i^2=250000\\\\\\i=500$

To the nearest tenth we have:   i=500

Ques 10)

A Pythagorean triple is the set of three positive integers a,b and c such that it satisfy:

                  $c^2=a^2+b^2$

Hence, we among the given above options the Pythagorean triple are:

 The last option form i.e. the triangle whose side is 300, 400 and i.

Also, the figure is attached to the answer.