Question

Can anyone help me please

Answer 1

Answer:

NM = $\sf \sqrt{70}$

Step-by-step explanation:

Let NM = y

If KL is twice the length of NM, then KL = 2y

Given:

• KM = 20
• NO = 7

As ΔKLN ~ ΔNOM

   KL : KM = NO : NM

$\sf \implies 2y : 20 = 7 : y$

$\sf \implies \dfrac{2y}{20}=\dfrac{7}{y}$

$\sf \implies 2y \cdot y=7 \cdot 20$

$\sf \implies 2y^2=140$

$\sf \implies y^2=70$

$\sf \implies y=\sqrt{70}$

As NM = y, then NM = $\sf \sqrt{70}$

Answer 2

Answer:

NM = $\sqrt{70}$

Step-by-step explanation:

Δ NMO and Δ KML are similar ( by the AA postulate )

Then the ratios of corresponding sides are in proportion, that is

$\frac{NM}{KM}$ = $\frac{NO}{KL}$ ( substitute values, noting KL = 2NM )

$\frac{KM}{29}$ = $\frac{7}{2NM}$ ( cross- multiply )

2 NM² = 140 ( divide both sides by 2 )

NM² = 70 ( take the square root of both sides )

NM = $\sqrt{70}$