The measure of the side PR and QR are 4cm and 8cm respectively. If the length of height PL with respect to the base QR is 5 CM., then find the height QM with respect to the base PR.
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Answers
║⊕QUESTION⊕║
The measure of the side PR and QR are 4 cm and 8 cm respectively. If the length of height PL with respect to the base QR is 5 CM, then find the height QM with respect to the base PR.
║⊕ANSWER⊕║
PL²+LR²=PR²
5² +LR² =8²
LR =√64-25
LR =√39
LR = 6.24 cm
Now,
LQ = 6.24-4
= 2.24 cm
IN TRIANGLE PLQ
PL²+LQ²=PQ²
5²+2.24²=PQ²
25+5.01=PQ²
PQ = 5.47cm
Area of triangle( PLR) = 1/2×B×H
=1/2×6.24×5
=15.6 cm²
Area of triangle(PLQ) = 1/2×B×H
= 1/2×2.24×5
= 5.6 cm²
Area of ∆PQR = 15.6-5.6
=10 cm²
1/2×8×QM = 10
QM = 10/4
QM = 2.5 cm