Question

Find the value of r.

Note: Write your answer as a decimal.

Answer 1

`\huge\boxed{\sf r = 10.5}`

Explanation:

Since it is a right-angled triangle, it has base, perpendicular and hypotenuse.

Base = r

Perpendicular = 14

Hypotenuse = r + 7

Using Pythagoras theorem:

`(Hypotenuse)^2 = (Base)^2+(Perp)^2`

Put the values

(r + 7)² = (r)² + (14)²

Using formula a² + 2ab + b² = (a + b)²

r² + 14r + 49 = r² + 196

Subtract r² to both sides

14r + 49 = 196

Subtract 49 to both sides

14r = 196 - 49

14r = 147

Divide 14 to both sides

r = 147 / 14

r = 10.5

`\rule[225]{225}{2}`