the perimeter and the length of the base of an isosceles triangle are 25 cm and 9 cm respectively. calculate the area of triangle
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The perimeter and the length of base of an isosceles triangle are 25 cm and 9 cm respectively. What is the area of the triangle?
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The perimeter and the length of base of an isosceles triangle are 25 cm and 9 cm respectively. What is the area of the triangle?
In an isosceles triangle, two sides have the same length and the third side has a different length. Only problem is, we don’t know from your question if the base is the unique side.
Case 1: The base is the unique side.
As the perimeter is the length of the three sides added together, the total length of the other sides must be equal to the perimeter less the length of the base = 25 cm - 9 cm = 16 cm. As these sides are of equal length, they must both be 8 cm long.
Case 2: The base is not the unique side.
As the base is not unique, one of the other sides is also 9 cm long, which means that the third (unique) side is of length 25 cm - 18 cm = 7 cm.
Calculation time.
Case 1:
By Pythagoras: AC2=AD2+CD2⇒CD2=AC2−AD2
=82−4.52=64−20.25=43.75=1754
⇒CD=1754−−−√=527–√
The area of the triangle ABC is half the distance AB multiplied by the distance CD (half base times height), thus:
Area=92×527–√=4547–√
≈29.76470224948
Answer: approx. 29.764 702 249 sq.cm
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Answer:
Since it's an isosceles triangle
both the sides will be of equal length
let both the equal sides be 2x
thus
perimeter =sum of all the sides
25 cm=9 +2x
25 cm -9 cm =2x
16=2x
x=8cm
Step-by-step explanation:
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