Chapter 8: Q2. (page 291)

Which equations are correct for the right triangle shown ?
$\begin{array}{l} (a) . r^{2} = s^{2} + t^{2} (b) . s^{2} = r^{2} + t^{2} (c) . s^{2} + r^{2} = t^{2} \\ (d) . s^{2} = t^{2} - r^{2} (e) . t = r + s (f) . t^{2} = {(r + s)}^{2} \end{array}$

Short Answer

Expert verified

The correct equation is,

$t^{2} = r^{2} + s^{2}$

Step by step solution

Step 1. Given information.

We have given a figure as shown below.

Step 2. Use Pythagorean Theorem.

From Pythagorean Theorem we know that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.

Step 3. The given triangle is right triangle.

Therefore,

$t^{2} = r^{2} + s^{2}$

It can also be written as,

$s^{2} = t^{2} - r^{2}$

Therefore, the correct equation is option $(d) .$

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Which equations are correct for the right triangle shown ?
$\begin{array}{l} (a) . r^{2} = s^{2} + t^{2} (b) . s^{2} = r^{2} + t^{2} (c) . s^{2} + r^{2} = t^{2} \\ (d) . s^{2} = t^{2} - r^{2} (e) . t = r + s (f) . t^{2} = {(r + s)}^{2} \end{array}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use Pythagorean Theorem.

Step 3. The given triangle is right triangle.

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Which equations are correct for the right triangle shown ?a.r2=s2+t2b.s2=r2+t2c.s2+r2=t2d.s2=t2−r2e.t=r+sf.t2=r+s2

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Use Pythagorean Theorem.

Step 3. The given triangle is right triangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Pure Maths

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Statistics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Which equations are correct for the right triangle shown ?
$\begin{array}{l} (a) . r^{2} = s^{2} + t^{2} (b) . s^{2} = r^{2} + t^{2} (c) . s^{2} + r^{2} = t^{2} \\ (d) . s^{2} = t^{2} - r^{2} (e) . t = r + s (f) . t^{2} = {(r + s)}^{2} \end{array}$