ꕔPQR ~ ꕔUTS. If A(ꕔPQR) : A(ꕔUTS) = 16 : 9, and TS =1.8 cm, then QR=
Answers
Step-by-step explanation:
Given :-
ꕔPQR ~ ꕔUTS.
A(ꕔPQR) : A(ꕔUTS) = 16 : 9
TS =1.8 cm
To find :-
Find the value of QR ?
Solution :-
Given that
ꕔPQR and ꕔUTS are two similar triangles.
The ratio of area of two triangles = 16:9
A(ꕔPQR) : A(ꕔUTS) = 16 : 9
The length of TS = 1.8 cm
We know that
" The ratio of areas of two similar triangles is equal to the ratio of the squares of the lengths of the corresponding sides".
=> Area(∆PQR)/Area(∆UTS)
=> (PQ/UT)² = (QR/TS)² = (PR/US)²
Now,
According to the given problem
=> Area(∆PQR)/Area(∆UTS) = (QR/TS)²
=> 16/9 = (QR/1.8)²
=>√(16/9) = QR/1.8
=> 4/3 = QR/1.8
On applying cross multiplication then
=> 4×1.8 = 3×QR
=> 7.2 = 3QR
=> 3QR = 7.2
=> QR = 7.2/3
=> QR = 2.4 cm
Therefore, QR = 2.4 cm
Answer:-
The value of QR for the given problem is 2.4 cm
Used formulae:-
" The ratio of areas of two similar triangles is equal to the ratio of the squares of the lengths of the corresponding sides".
