Question

Jayden and Sheridan both tried to find the missing side of the right triangle. A right triangle is shown. One leg is labeled as 7 centimeters. The hypotenuse is labeled as 13 centimeters.Jayden's WorkSheridan's Worka2 + b2 = c2a2 + b2 = c272 + 132 = c272 + b2 = 13249 + 169 = c249 + b2 = 169218 = c2b2 = 120Square root 218 equals square root c squared.Square root b squared equals square root 120.14.76 ≈ cb ≈ 10.95Is either of them correct? Explain your reasoning

Answer 1

Sheridan's Work is correct

Explanation:

we know that

The lengths side of a right triangle must satisfy the Pythagoras Theorem

`c^(2)=a^(2)+b^(2)`

where

a and b are the legs

c is the hypotenuse (the greater side)

In this problem

Let

`a=7\ cm\\c=13\ cm`

substitute

`13^(2)=7^(2)+b^(2)`

Solve for b

`169=49+b^(2)`

`b^(2)=169-49`

`b^(2)=120`

`b=√(120)\ cm`

`b=10.95\ cm`

we have that

Jayden's Work

`a^(2)+b^(2)=c^(2)`

`a=7\ cm\\b=13\ cm`

substitute and solve for c

`7^(2)+13^(2)=c^(2)`

`49+169=c^(2)`

`218=c^(2)`

`c=√(218)\ cm`

`c=14.76\ cm`

Jayden's Work is incorrect, because the missing side is not the hypotenuse of the right triangle

Sheridan's Work

`a^(2)+b^(2)=c^(2)`

`a=7\ cm\\c=13\ cm`

substitute

`7^(2)+b^(2)=13^(2)`

Solve for b

`49+b^(2)=169`

`b^(2)=169-49`

`b^(2)=120`

`b=√(120)\ cm`

`b=10.95\ cm`

therefore

Sheridan's Work is correct