In a given parallelogram PQRS,ST is altitude to the base PQ. The area of PQRS is 120cm square. if PQ=15 cm , PT=6cm , find ST and SP
Answers
The length of ST is 8 cm and SP is 10 cm.
Step-by-step explanation:
It is given that,
PQRS is a parallelogram
ST is the altitude to base PQ
PQ = 15 cm
PT = 6 cm
Area of PQRS = 120 cm²
Case 1: Finding the length of ST
We know that the formula of the area of a parallelogram, we get
Area = base * altitude
Substituting the given values in the formula above, we get
Area = PQ * ST
⇒ 120 = 15 * ST
⇒ ST = 120/15
⇒ ST = 8 cm
Thus, the length of ST is 8 cm.
Case 2: Finding the length of SP
Consider right ∆PST, by applying Pythagoras theorem, we get
SP² = ST² + PT²
⇒ SP = √[8² + 6²]
⇒ SP = √ [64 + 36]
⇒ SP = √100
⇒ SP = 10 cm
Thus, the length of SP is 10 cm.
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