Question

△PQR ~ △KLM, 16 × A (△KLM) = 25 × A (△PQR). If QR = 28 units. ML = ?​

Answer 1

Answer:

ML=35units

Step-by-step explanation:

Given that;∆PQR~∆KLM

16×A(∆KLM)=25×(∆PQR)

& QR=28 ML=??

So,

16×A(∆KLM)=25×A(∆PQR)

A(∆KLM)/A(∆PQR)=25/16

ML²/QR²=5²/4²

ML/QR=5/4

ML=5/4×QR

ML=5/4×28 {QR=28}

ML=5×7

ML=35units

I hope it is helpful.....

Answer 2

Answer:

The length of LM is 35 units

Step-by-step explanation:

Given that :

• ΔPQR ≈ ΔKLM
• 16 * Area of ΔKLM = 25 * Area of ΔPQR           --(i)
• QR = 28 units

To find:

Length of ML

As it is given that ΔPQR ≈ ΔKLM

Therefore, we know that the for two similar triangles, the ratio of their areas is equal to the square of their corresponding sides.

=> $\frac{Area of KLM}{Area of PQR}$  = $(\frac{KL}{PQ})^2$ = $(\frac{LM}{QR})^2$ = $(\frac{KM}{PR})^2$                       --(ii)

 From equation (i), we can say that  $\frac{Area of KLM}{Area of PQR}$ = $\frac{25}{16}$

On substituting the given values in equation (ii), we get,

 $\frac{25}{16}$ = $(\frac{LM}{28})^2$

=>   $(\frac{5}{4})^2$ = $(\frac{LM}{28})^2$

Taking square root both sides,

=>  $\frac{5}{4}$ = $\frac{LM}{28}$

=> LM = $\frac{5*28}{4}$

=> LM = 35 units

Therefore, the length of LM is 35 units