Question

To the nearest hundredth of a centimeter, what is the length of a leg of the triangle?

[1] cm
84.6 cm

Answer 1

The length of a leg of the triangle = 59.83 cm

Explanation:

Points to remember

If a right angled triangle with angles 45°, 45° and 90° then the sides are in ratio 1 : 1 : √2

It is given a right angled triangle with 45°, 45° and 90° and hypotenuse = 84.6 cm

To find the length of a leg

Let 'x' be the length of each leg,

From the figure we can write,

1: 1 : √2 = x : x : 84.6

Therefore x = 84.6/√2

= 59.83 cm

Therefore the length of a leg of the triangle = 59.83 cm

Answer 2

59.82

EXPLANATION

The given right angle is an isosceles right triangle.

Let the length of a leg be x cm.

Then by the Pythagoras Theorem,

`{x}^(2) + {x}^(2) = 84.6 ^(2)`

`2 {x}^(2) = 7157.16`

Divide both sides by 2.

`{x}^(2) = (7157.16)/(2)`

`{x}^(2) = 3578.58`

Take positive square root of both sides to get,

`x = 59.82123369`

Hence the length of a leg is 59.82 to the nearest hundredth.