Question

solve the following problem

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Question:

ABC is an isosceles triangle with AB = AC = 10 cm. The height AD from A to B is 5.5 cm. Find the area of ABC. What will be the height from C to AB?

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Solution:

In triangle ABD,

• AB = 10 cm

• AD = 5.5 cm

• AD is height. Angle ADB = 90°

So,

Applying Pythagoras theorem in triangle ADB,

AD² + BD² = AB²

=> (5.5 cm)² + BD² = (10 cm)²

=> BD² = (10 - 5.5 cm)(10 + 5.5 cm)

=> BD² = 69.75 cm²

=> BD = 8.352 cm

We know that, in an isosceles triangle, the altitude drawn from the common vertex of equal sides perpendicular to the unequal side is also the median of the third side. In other words, AD is the altitude as well as the median of side BC.

So,

BC = 2 * BD

=> BC = 2 * 8.352 cm

=> BC = 16.704 cm

We know that,

Area = (1/2) * base * height

=> Area = (1/2) * BC * AD

=> Area = (1/2) * 16.704 * 5.5 cm²

=> Area = 45.936 cm²

Considering base as AB and height as the altitude from C to AB,

Area = (1/2) * base * height

=> Area = (1/2) * AB * altitude from C to AB

=> Area = (1/2) * 10 cm * altitude from C to AB

We have already found the value of area.

=> 45.936 cm² = 5 cm * altitude form C to AB

=> altitude from C to AB = 9.1872 cm