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An isosceles triangle has sides that are5cm,5cmand8cmlong. Find its area and the lengths of the three altitudes.

Short Answer

Expert verified

The area of triangle is12โ€‰โ€‰sq.โ€‰โ€‰unit and the length of altitudes are 3,4.8,4.8

Step by step solution

01

Step 1. Draw the diagram.

02

Step 2. Concept used.

We can use Pythagorean Theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

52=42+h2h2=25โˆ’16h2=9h=3

03

Step 3. Use the concept of area of triangle.

Area of โ–ณABCcan be found using the formula

b=BC=8h=3A=12bhA=12(8)(3)A=12โ€‰โ€‰sq.โ€‰โ€‰unit

04

Step 4. Find the altitudes.

The length of altitudeBE

b=5h=?A=12A=12bh12=12(5)(h)24=5hh=245h=4.8

Similarly, The length of altitudeCF is4.8

Therefore, the Area is12โ€‰โ€‰sq.โ€‰โ€‰unit

The length of altitudes are3,4.8,4.8.

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