Question

PQR = STU .QR=8 TU =12cm A(trianglePQR) =128cm2 find A(triangle STU)​

Answer 1

Answer:

as triangle pqr is similar to triangle stu

So, by area ratio theorem

$\frac{area \: of \: pqr}{area \: of \: stu} = \frac{ {qr}^{2} }{ {tu}^{2} } \\ \frac{128}{area \: of \: stu} = \frac{ {8}^{2} }{ {12}^{2} } \\ area \: of \: stu \: = 288 \: {cm}^{2}$

Answer 2

A(triangle STU)​ is 288 cm².

------------------------------------------------------------------------------------------

Let's understand a few concepts:

To find Area(triangle STU)​ we must use the Theorem of Areas of Similar Triangles.

What are similar triangles?

Two triangles are said to be similar if their corresponding angles are equal and their corresponding sides are proportional to each other.

What is the Theorem of Areas of Similar Triangles?

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

For example: if ΔABC and ΔPQR are two similar triangles then we can say that,

$\boxed{\bold{\frac{Area(\triangle ABC)}{Area(\triangle PQR)} = \bigg(\frac{AB}{PQ} \bigg)^2 = \bigg(\frac{BC}{QR} \bigg)^2 = \bigg(\frac{AC}{PR} \bigg)^2}}$

---------------------------------------------------------------------------------------------

Let's solve the given problem:

Δ PQR ~ ΔSTU

QR = 8 cm

TU = 12 cm

Area (Δ PQR) = 128 cm²

By using the above theorem of the areas of similar triangles, we get

$\frac{Area(\triangle PQR)}{Area(\triangle STU)} = \bigg(\frac{QR}{TU} \bigg)^2$

$\implies \frac{128}{Area(\triangle STU)} = \bigg(\frac{8}{12} \bigg)^2$

$\implies \frac{128}{Area(\triangle STU)} = \frac{64}{144}$

$\implies Area(\triangle STU) = \frac{128\:\times\: 144}{64}$

$\implies Area(\triangle STU) =2\:\times\: 144$

$\implies \bold{Area(\triangle STU) = 288\:cm^2}$

Thus, the area of triangle STU is 288 cm².

----------------------------------------------------------------------------------------

Learn more about this topic from brainly.in:

brainly.in/question/180664

brainly.in/question/28614466