Question

Please solve q 52 ?

Answer 1

`23.2` units

Explanation:

If three sides of a triangle are known, we can use Heron's formula to find the area of the triangle,
`A=sqrt(s(s-a)(s-b)(s-c))`,
where `s=(a+b+c)/2, and a,b, and c` are the lengths of the sides of the triangle.
Let `|PQR|` be area of `DeltaPQR`,
given `PQ=10, PR=17, and QR=21`,
`s=(10+17+21)/2=24`
`=> |PQR|=sqrt(24(24-10)(24-17)(24-21))=sqrt(24*14*7*3)=84 " units"^2`
`|PQR|=1/2*QR*PE=1/2*21*PE=84`,
`=> PE=(84xx2)/21=8` units
let `AB=AD=x, => FE=x`
`=> PF=PE-FE=8-x`
`DeltaPAB and DeltaPQR` are similar,
`=> (PF)/(AB)=(PE)/(QR)`,
`=> (8-x)/x=8/21`
`=> 29x=168, => x=168/29` units,
Hence, perimeter of square `ABCD=4x=4*168/29~~23.2` units