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Chapter 11: Q. 82 (page 774)

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

Expert verified

The length of its base is 8cm.

Step by step solution

01

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,

4a2-b22=34a2-b2=64a2-b2-36=0......(i)

Perimeter of the isosceles triangle,

2a+b=182a+b-18=0......(ii)

Solve equation (ii) for b,

b=18-2a......(iii)

02

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

Substitute the value of bin equation (i),

4a2-18-2a2-36=04a2-324-72a+4a2-36=072a-360=0a=5

Substitute the value of a in equation (iii),

role="math" localid="1646850774031" b=18-25b=18-10b=8

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