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

Answer:

$\bold{\sqrt{75}}$

Step-by-step 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:

$\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow GJ^{2} = GH^{2} + HJ^{2}\\\Rightarrow 10^2=5^2+HJ^2\\\Rightarrow HJ = \sqrt{100-25}\\\Rightarrow \bold{HJ = \sqrt{75}}$