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2 years ago

In kite PQRS , TQ=5 cm and TR=12 cm. What is SR ? Enter your answer in the box.

Mathematics

1 answer:

ozzi2 years ago

3 0

The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.
You can use Pythagoras' Theorem to calculate QR:
a^2 + b^2 = c^2
5^2 + 12^2 = QR^2
25 + 144 = QR^2
169 = QR^2
This means that the square root of 169cm is QR, which is 13cm.

SR is equal to QR, which means that SR is 13cm.

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2 years ago

. In triangle JKL, ∠ J measures 25.8º, and ∠ K is a right angle. What is the measure of ∠ L?

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2 years ago

Line segment JL is an altitude in triangle JKM. Which statement explains whether JKM is a right triangle? Round measures to the

natulia [17]

Answer:

C. JKM is not a right triangle because KM ≠ 15.3.

Step-by-step explanation:

We can see from our diagram that triangle JKM is divided into right triangles JLM and JLK.

In order to triangle JKM be a right triangle $KM^{2}=JK^{2}+JM^{2}$ .

We will find length of side KM using our right triangles JLM and JLK as $KM=KL+LM$ .

Using Pythagorean theorem in triangle JLM we will get,

$LM=\sqrt{JM^{2}-JL^{2}}$

$LM=\sqrt{8^{2}-5^{2}}$

$LM=\sqrt{64-25}$

$LM=\sqrt{39}=6.244997998\approx 6.24$

Now let us find length of side KL.

$KL=\sqrt{JK^{2}-JL^{2}}$

$KL=\sqrt{13^{2}-5^{2}}$

$KL=\sqrt{169-25}$

$KL=\sqrt{144}=12$

Now let us find length of KM by adding lengths of KL and LM.

$KM=12+6.24=18.24$

Now let us find whether JKM is right triangle or not using Pythagorean theorem.

$KM^{2}=JK^{2}+JM^{2}$

$18.24^{2}=13^{2}+8^{2}$

$18.24^{2}=169+64$

$18.24^{2}=233$

Upon taking square root of both sides of equation we will get,

$18.24\neq 15.264337522473748$

$18.2\neq 15.3$

We have seen that KM equals 18.2 and in order to JKM be a right triangle KM must be equal to 15.3, therefore, JKM is not a right triangle and option C is the correct choice.

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2 years ago

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Eli is thinking of two numbers. If you add them, the answer is 13. If you subtract them, the answer is 3. What is one of the two

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2 years ago

In ​ kite PQRS ​, TQ=5 cm and TR=12 cm. What is SR ? Enter your answer in the box.

In kite PQRS , TQ=5 cm and TR=12 cm. What is SR ? Enter your answer in the box.