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Altitudes

Solve the first problem 14 problems

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1. Altitude of an isosceles triangle ●○○○○ 10 ptsIn triangle $ABC$ with $AB=AC=25$ and $BC=14$, let $D$ be the foot of the altitude from $A$ to $BC$. Find the length of $AD$.
2. Altitude of an equilateral triangle ●○○○○ 10 ptsAn equilateral triangle has side length 6 cm. Find the length of its altitude. Round to two decimal places.
3. Right triangle with given circumradius and altitude ●○○○○ 10 ptsA right-angled triangle has circumradius $3$ cm. The altitude drawn to its hypotenuse is $2$ cm. Find the area of the triangle in square centimetres.
4. Shortest altitude of a triangle ●●○○○ 20 ptsThe sides of a triangle have lengths $15$, $20$, and $25$. Find the length of the shortest altitude.
5. Minimum area with given hypotenuse altitude ●●○○○ 20 ptsIn right triangle $ABC$, the altitude to the hypotenuse has length 4. Find the minimum value of the area of triangle $ABC$.
6. Triangle sides from heights ●●○○○ 20 ptsIn triangle $ABC$, the height to side $a$ is $6$ cm and the height to side $b$ is $9$ cm. Side $a$ is $4$ cm longer than side $b$. Calculate the side lengths $a$ and $b$ (in cm).

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