Question

If the areas of two similar triangles are in the ratio of 49:100. Triangle ABC ~ Triangle PQR. BC = 2.5. Find QR

Answer 1

*Correct Question:—

The areas of two similar triangles ABC and PQR are 25 cm2 and 49 cm2 respectively. If QR = 9.8 cm, then BC is :

Answer:—

Value of BC = 7cm

Step-by-step explanation:—

Theorem:—

→ The ratio of the areas of two similar triangles is equal to the ratio of the squares of their corresponding sides.

Here,

→ area of ∆ABC = 25 cm²,

→ area of ∆PQR = 49 cm²,

→ QR = 9.8 cm

→ BC = ?

$\frac{area\:of \triangle ABC}{area\:of \triangle PQR}=\left(\frac{BC}{QR}\right)^{2}$

$\implies \frac{25}{49}=\left(\frac{BC}{9.8}\right)^{2}$

$\implies \left(\frac{5}{7}\right)^{2}=\left(\frac{BC}{9.8}\right)^{2}$

$\implies \frac{5}{7}=\frac{BC}{9.8}$

$\implies \frac{5\times 9.8}{7}$

$\implies 5\times 1.4=BC$

$\implies 7=BC$

Therefore,

$Value \:of \: BC = 7 \:cm$

$@vikram$