Question

Pleaseee help
With #30
I have the answer but need the process bc it’s for a study guide

Answer 1

The value are give below:

What is Pythagoras theorem?

Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Using Pythagoras theorem in FPO

FO²= FP²+ OP²

FO²=12.5²+19²

FO²=39.75

FO= 22.74

Now In OQR

OR²=OQ²+QR²

517.25= x² +14²

x²= 321.25sx

x=17.9

31. Now, given triangle

    H² = 5²+10²

    H²=125

    H=11.18

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Answer 2

The value of x in the figure is 17.9

How to calculate the value of x in #30?

Considering the triangle FOP, where:

• FO ⇒ hypotenuse
• OP and PF ⇒ Legs of the triangle

From the question, we have:

OP = 19

FG = 25

Where:

FP = 0.5 * FG

FP = 0.5 * 25 = 12.5

Using Pythagoras theorem, we have:

FO² = FP² + OP²

Substitute known values

FO² = 12.5² + 19²

Evaluate the sum of squares

FO² = 517.25

Considering the triangle ROQ, where:

• OR = FO ⇒ hypotenuse
• OQ and RQ ⇒ Legs of the triangle

From the question, we have:

OQ = x

RS = 28

Where:

RQ = 0.5 * RS

RQ = 0.5 * 28 = 14

Using Pythagoras theorem, we have:

OR² = OQ² + RQ²

Recall that

OR = FO

Square both sides

OR² = FO²

This means that:

FO² = OQ² + RQ²

Substitute known values

517.25 = x² + 14²

Collect like terms

x² = 517.25 - 14²

Evaluate

x² = 321.25

Take the square root of both sides

x = 17.9

Hence, the value of x is 17.9

Read more about Pythagoras theorem at:

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