Question

Find the length of the third side. If necessary, write in simplest radical form.

Answer 1

8

Explanation:

Answer 2

`\boxed {\boxed {\sf 8}}`

Explanation:

This triangle has a small square, which represents a right angle. Therefore, we can use the Pythagorean Theorem.

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

Where a and b are the legs of the triangle and c is the hypotenuse.

In this triangle, 7 and √15 are the legs, because these sides make up the right angle. The unknown side is the hypotenuse, because it is opposite the right angle. So, we know two values:

`a= 7 \\b= √(15)`

Substitute these values into the formula.

`(7)^2+(√(15))^2=c^2`

Solve the exponents.

• (7)²= 7*7=49

`49+ (√(15))^2=c^2`

• (√15)²=√15*√15=15

`49+15=c^2`

Add.

`64=c^2`

Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.

`√(64)=√(c^2) \\√(64)= c\\8=c`

The third side length is 8.