Chapter 11: Q. 82 (page 774)

The altitude of an isosceles triangle drawn to its base is $3 c m$ , and its perimeter is $18 c m$ . Find the length of its base.

Short Answer

Expert verified

The length of its base is $8 c m$ .

Step by step solution

Step 1. Given information.

Assume b to be the base of the isosceles triangle and one of the equal sides isa.

Height of the isosceles triangle,

$\frac{\sqrt{4 a^{2} - b^{2}}}{2} = 3 \sqrt{4 a^{2} - b^{2}} = 6 4 a^{2} - b^{2} - 36 = 0 . . . . . . (i)$

Perimeter of the isosceles triangle,

$2 a + b = 18 2 a + b - 18 = 0 . . . . . . (i i)$

Solve equation (ii) for b,

$b = 18 - 2 a . . . . . . (i i i)$

Step 2. Substitute the value of b in equation (i).

Substitute the value of bin equation (i),

$4 a^{2} - {(18 - 2 a)}^{2} - 36 = 0 4 a^{2} - (324 - 72 a + 4 a^{2}) - 36 = 0 72 a - 360 = 0 a = 5$

Substitute the value of a in equation (iii),

role="math" localid="1646850774031" $b = 18 - 2 (5) b = 18 - 10 b = 8$

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The altitude of an isosceles triangle drawn to its base is $3 c m$ , and its perimeter is $18 c m$ . Find the length of its base.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of b in equation (i).

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The altitude of an isosceles triangle drawn to its base is 3cm, and its perimeter is 18cm. Find the length of its base.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute the value of b in equation (i).

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Geometry

Applied Mathematics

Theoretical and Mathematical Physics

Mechanics Maths

Statistics

Study anywhere. Anytime. Across all devices.

The altitude of an isosceles triangle drawn to its base is $3 c m$ , and its perimeter is $18 c m$ . Find the length of its base.