Chapter 8: Q. 19 (page 541)

Find the area of a triangle whose sides are $a = 12, b = 13, c = 5$ .

Short Answer

Expert verified

Required area of the triangle is 30 square units.

Step by step solution

Step 1. Given information

The area of a triangle with sides a, b, and c is determined by the Heron's formula which is given as:

$A r e a = \sqrt{s (s - a) (s - b) (s - c)}$

where, $s = \frac{a + b + c}{2}$

Step 2. Calculation

Given,

$a = 12, b = 13, c = 5 T h e n, s = \frac{a + b + c}{2} = \frac{12 + 13 + 5}{2} = 15 N o w, H e r o n' s F o r m u l a g i v e s a r e a a s A r e a = \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{15 (15 - 12) (15 - 13) (15 - 5)} = \sqrt{15 \times 3 \times 2 \times 10} = \sqrt{900} = 30 s q u a r e u n i t s$

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Find the area of a triangle whose sides are $a = 12, b = 13, c = 5$ .

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

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Find the area of a triangle whose sides area=12,b=13,c=5.

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Logic and Functions

Pure Maths

Geometry

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find the area of a triangle whose sides are $a = 12, b = 13, c = 5$ .