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.