Chapter 11: Q29. (page 432)

a. Find the ratio of the areas of $△ Q R T$ and $△ Q T S$ .
b. If the area of $△ Q R S$ is240. Find the length of the altitude from sto. $\overset{\leftrightarrow}{Q R}$

Short Answer

Expert verified

a.The ratio of the areas of $△ Q R T$ and $△ Q T S$ is $2 : 3$ .

b. The altitude from s to $Q R$ is 240.

Step by step solution

Step 1. Given information.

$Q R = 24, R T = 12$ and $T S = 18$

Step 2. Concept Used.

Area of triangle can be found using the formula

$A = \frac{1}{2} b h$

Whereb= base of triangle andh= height of triangle.

Step 3. Find the area of triangles.

Area of triangle $△ Q R T$ is

$\begin{array}{l} b = R T = 12 \\ h = h \\ A = \frac{1}{2} b h \\ A = \frac{1}{2} (12) (h) \\ A (Q R T) = 6 h \end{array}$

Area of triangle $△ Q T S$ is

$\begin{array}{l} b = T S = 18 \\ h = h \\ A = \frac{1}{2} b h \\ A = \frac{1}{2} (18) (h) \\ A (Q T S) = 9 h \end{array}$

Step 4. Find the ratio of areas.

So, the ratio of the areas of $△ Q R T$ and $△ Q T S$ will be

$\begin{matrix} \frac{A (Δ Q R T)}{A (Δ Q T S)} = \frac{6 h}{9 h} \\ = \frac{2}{3} \\ = 2 : 3 \end{matrix}$

Therefore, the ratio of the areas of $△ Q R T$ and $△ Q T S$ is $2 : 3$ .

Step 1. Given information.

Area of $△ Q R S = 240$

Let the altitude be x

Step 2. Concept Used.

Area of triangle can be found using the formula

$A = \frac{1}{2} b h$

Where b= base of triangle and h=height of triangle.

Step 3. Use the formula of the area of triangle.

$\begin{array}{l} b = Q R = 24 \\ h = x \\ A = \frac{1}{2} b h \\ A = \frac{1}{2} (24) (x) \\ A (Q R S) = 12 x \\ 240 = 12 x \\ x = 20 \end{array}$

Therefore, the altitude from s to $Q R$ is 20.

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a. Find the ratio of the areas of $△ Q R T$ and $△ Q T S$ .
b. If the area of $△ Q R S$ is240. Find the length of the altitude from sto. $\overset{\leftrightarrow}{Q R}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Find the area of triangles.

Step 4. Find the ratio of areas.

Step 1. Given information.

Step 2. Concept Used.

Step 3. Use the formula of the area of triangle.

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a. Find the ratio of the areas of△QRTand△QTS.b. If the area of△QRSis240. Find the length of the altitude from sto.QR↔

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Find the area of triangles.

Step 4. Find the ratio of areas.

Step 1. Given information.

Step 2. Concept Used.

Step 3. Use the formula of the area of triangle.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Applied Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

a. Find the ratio of the areas of $△ Q R T$ and $△ Q T S$ .
b. If the area of $△ Q R S$ is240. Find the length of the altitude from sto. $\overset{\leftrightarrow}{Q R}$