In a triangle ABC, AB = BC = 7 and AC = 4, and BD is the medain of the triangle, find the length of BD.

Given in a triangle ABC, BD is the median, and sides AB = 7, BC = 7, AC = 4.

The median of the triangle is given by

\$BD = \sqrt{\frac{2(BC) ^2 + 2(AB) ^2 - (AC) ^2}{4}} \$

Substitute the values.

\$\Rightarrow BD = \sqrt{\frac{2(7) ^2 + 2(7) ^2 - (4) ^2}{4}} \$

Calculate the exponents.

\$\Rightarrow BD = \sqrt{\frac{2(49) + 2(49) - 16}{4}} \$

Multiply.

\$\Rightarrow BD = \sqrt{\frac{98 + 98 - 16}{4}} \$

Add and subtract.

\$\Rightarrow BD = \sqrt{\frac{180}{4}} \$

Cancel out commom factor.

\$\Rightarrow BD = \sqrt{\frac{\cancel{180} ^{45}}{\cancel{4} ^1}} \$

Answer

The value of the median BD of triangle ABC = \$\sqrt{45}\$.