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CBSE Class 9 Answered

Calculate the area of an isosceles triangle with equal sides of measure 13 cm and third side of measure 24 cm.
Asked by Topperlearning User | 28 Aug, 2017, 03:04: PM
answered-by-expert Expert Answer

begin mathsize 12px style Given colon space PQ equals space PR space equals space 13 space cm space and space QR space left parenthesis l right parenthesis equals 24 space cm
In space increment PQR comma space draw space PM perpendicular QR
rightwards double arrow QM equals 12 space cm comma space since space QM equals MR
We space know space that space PMQ space is space straight a space right space triangle
Therefore comma space by space using space Pythagoras space Theorem comma space we space can space find space the space length space PM
as space shown space below colon
PQ squared equals PM squared plus QM squared
13 squared equals PM squared plus 12 squared
PM squared equals 25 space cm squared
PM equals 5 space cm
PM space left parenthesis straight h right parenthesis space equals space 5 space cm
Then space area space of space increment PQR space equals space 1 half cross times straight b cross times straight h equals 1 half cross times 24 cross times 5 equals 60 space cm squared end style

Answered by | 28 Aug, 2017, 05:04: PM
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