`DeltaABC~anglePQR`, दिया गया हे, यदि `("क्षेत्रफल"(DeltaPQR))/("क्षेत्रफल"(DeltaABC))=256/441` हे और PR=12 सेमी. हे तो AC किसके बराबर होगा?

Options

A. `12sqrt(2)` cm
B. 15.5 cm
C. 16 cm
D. 15.75 cm

Answer

D

Explanation

`therefore DeltaPQR ~ DeltaABC`
`rArr` We know that in similar triangle
`rArr ("Area of triangle1")/("area of triangle") = ("Corresponding side 1")/("corresponding side 2")`
`rArr (DeltaPQR)/(DeltaABC) = 256/441`
`rArr` `(DeltaPQR)/(DeltaABC) = (PR)^(2)/(AC)^(2)`
`256/441=(12)^(2)/(AC)^(2)`
`rArr (16/21)^(2)=(12/AC)^(2)`
`rArr 16/21 = 12/AC`
`4/21= 3/AC`
`rArr AC=63/4`
`rArr AC =15.75` cm