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 Work Sheridan's Work
a2 + b2 = c2 a2 + b2 = c2
72 + 132 = c2 72 + b2 = 132
49 + 169 = c2 49 + b2 = 169
218 = c2 b2 = 120
Square root 218 equals square root c squared. Square root b squared equals square root 120.
14.76 ≈ c b ≈ 10.95

Is either of them correct? Explain your reasoning

Answer 1

Sheridan's Work is correct

we know that

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

where

a and b are the legs

c is the hypotenuse (the greater side)

In this problem

Let

substitute

Solve for b

we have that

Jayden's Work

substitute and solve for c

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

Sheridan's Work

substitute

Solve for b

therefore

Sheridan's Work is correct