Question

Consider triangle GHJ. Triangle G H J is shown. Angle G H J is a right angle. The length of the hypotenuse is 10 and the length of another side is 5. What is the length of line segment HJ?

Answer 1

hJ = B 5 route 3

Explanation:

got it right on edg 2020-2021

Answer 2

`\bold{√(75)}`

Explanation:

Given

A
`\triangle GHJ` in which

`\angle GHJ = 90^\circ`

Hypotenuse = 10

Length of another side = 5

To find:

HJ = ?

Solution:

Kindly refer to the image attached in the answer area.

We know that there are only 3 sides in a triangle.

We are given hypotenuse is 10.

i.e. GJ = 10

To find HJ, Base = ?

So, we are given the side length of GH, perpendicular i.e. 5.

Kindly refer to attached image for further details.

Let us use Pythagorean theorem here.

According to Pythagorean theorem:

`\text{Hypotenuse}^(2) = \text{Base}^(2) + \text{Perpendicular}^(2)\\\Rightarrow GJ^(2) = GH^(2) + HJ^(2)\\\Rightarrow 10^2=5^2+HJ^2\\\Rightarrow HJ = √(100-25)\\\Rightarrow \bold{HJ = √(75)}`