Mathematics: What is the length of side ts? 2 is the square root of 6 units6 is the square root of 6 units 24 units 8 units

What is the length of side ts? 2 is the square

Ответ:

snoopyqueen2597

11.01.2022

Mathematics

In triangle TQS the length of the TS = $2\sqrt{6}$ units. Therefore the correct option is A).

Given :

RS = 12QR = 6TS = 3xTriangle TQS and triangle TRS are right angle triangles.

Solution :

In triangle TQS applying pythagorean theorem.

$\rm QS^2=TS^2+TQ^2$

$\rm 18^2 = (3x)^2+TQ^2$

$\rm TQ^2=324-9x^2$ ---- (1)

In triangle TRS applying pythagorean theorem.

$\rm TR^2+RS^2=TS^2$

$\rm TR^2+12^2=(3x)^2$

$\rm TR^2 = -144+9x^2$ ---- (2)

In triangle TRQ applying pythagorean theorem.

$\rm TQ^2=TR^2+QR^2$

$\rm TQ^2=TR^2+6^2$ --- (3)

Substitute the value of $\rm TQ^2\;and\;TR^2$ from equation (1) and (2) in equation (3)

324-9x^2=-144+9x^2+36

432=18x^2

x^2 = 24

$x=2\sqrt{6}$ units

In triangle TQS the length of the TS = $2\sqrt{6}$ units. Therefore the correct option is A).

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Ответ:

maddie7155

11.01.2022

Mathematics

We know that

in the triangle TQS
applying the Pythagorean theorem
QS²=TS²+TQ²> TQ²=QS²-TS²> TQ²=18²-9x²> equation 1

in the triangle TRS
TS²=TR²+RS²> TR²=TS²-RS²> TR²=9x²-144> equation 2

in the triangle QTR
TQ²=TR²+36> equation 3

I substitute 1 and 2 in 3
18²-9x²=9x²-144+36> 18x²-432=0> x²=24> x=√24
x=2√6
TS=3*x> 3*2√6> 6√6
TS=6√6 units

the answer is
TS=6√6 units
6 is the square root of 6 units

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Ответ:

blair454

05.04.2023

Mathematics

The difference is 5/12.

Step-by-step explanation:

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What is the length of side ts?
2 is the square root of 6 units
6 is the square root of 6 units
24 units
8 units

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