Question

What is the length of the unknown leg in the right triangle?

A) 6mm
B) 8mm
C) sqrt 78mm
D) sqrt 134mm

Answer 1

6mm

Explanation:

In a right angled triangle if a and b is the length of sides containing right angle, then length of hypotenuse is given by
`hypotenuse= √(a^2 + b^2)` .

In the given problem a and b are a and 7mm respectively.

hypotenuse =
`√( 85)`

Using the formula for hypotenuse we have

`hypotenuse= √(a^2 + b^2)\\\\\=>√(85) = √(a^2 + 7^2) \\ squaring / both / side / we / have\\=>√(85)^2 = √(a^2 + 7^2)^2\\=>85 = a^2 + 49\\\\=> a^2 = 85-49 = 36\\=>√(a^2) = √(36) \\=> a = 6`

Thus, length of unknown leg is 6mm.