Question
$\triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}, \mathrm{A}(\triangle \mathrm{ABC})=16, \mathrm{~A}(\triangle \mathrm{PQP})=25$, then find the value of ratio $\frac{\mathrm{AB}}{\mathrm{PQ}}$.
✓
Answer
$: \triangle \mathrm{ABC} \sim \triangle \mathrm{PQR}$
$\therefore \frac{\mathrm{A}(\triangle \mathrm{ABC})}{\mathrm{A}(\Delta \mathrm{PQR})}=\frac{\mathrm{AB}^2}{\mathrm{PQ}^2}\text{ .......... theorem of areas of similar triangles}$
$\therefore \frac{16}{25}=\frac{\mathrm{AB}^2}{\mathrm{PQ}^2} \quad \therefore \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{4}{5}\text{.......... taking square roots} $
theorem of areas of similar triangles taking square roots
$\therefore \frac{\mathrm{A}(\triangle \mathrm{ABC})}{\mathrm{A}(\Delta \mathrm{PQR})}=\frac{\mathrm{AB}^2}{\mathrm{PQ}^2}\text{ .......... theorem of areas of similar triangles}$
$\therefore \frac{16}{25}=\frac{\mathrm{AB}^2}{\mathrm{PQ}^2} \quad \therefore \frac{\mathrm{AB}}{\mathrm{PQ}}=\frac{4}{5}\text{.......... taking square roots} $
theorem of areas of similar triangles taking square roots
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
→→→→→→
Solve the following quadratic equation by factorization.
m2 - 11 = 0
m2 - 11 = 0
Prove the following trigonometric identities.
$\text{cos}^2\text{A}+\frac{1}{1+\cot^2\text{A}}=1$
→$\text{cos}^2\text{A}+\frac{1}{1+\cot^2\text{A}}=1$
If the distance between points $(x, 0)$ and $(0, 3)$ is $5$, what are the values of $x$?
→Write the coordinates of the point dividing line segment joining points (2, 3) and (3, 4) internally in the ratio 1 : 5.
If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b?
Find the sum of the following APs:
9, 7, 5, 3, .... to 14 terms.
9, 7, 5, 3, .... to 14 terms.
The lengths of the diagonals of a rhombus are $24\ cm$ and $10\ cm$. Find each side of the rhombus.
→Solve: $2x^2 + ax - a^2 = 0$
→Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.
One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.