Answer:
![\text{Length of AB is }\frac{ah}{a+h}](https://tex.z-dn.net/?f=%5Ctext%7BLength%20of%20AB%20is%20%7D%5Cfrac%7Bah%7D%7Ba%2Bh%7D)
Step-by-step explanation:
Given △KMN, ABCD is a square where KN=a, MP⊥KN, MP=h.
we have to find the length of AB.
Let the side of square i.e AB is x units.
As ADCB is a square ⇒ ∠CDN=90°⇒∠CDP=90°
⇒ CP||MP||AB
In ΔMNP and ΔCND
∠NCD=∠NMP (∵ corresponding angles)
∠NDC=∠NPM (∵ corresponding angles)
By AA similarity rule, ΔMNP~ΔCND
Also, ΔKAP~ΔKPM by similarity rule as above.
Hence, corresponding sides are in proportion
![\frac{ND}{NP}=\frac{CD}{MP} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{AB}{PM} \\\\\frac{ND}{NP}=\frac{x}{h} \thinspace\thinspace and\thinspace\thinspace \frac{KA}{KP}=\frac{x}{h}\\\\\frac{NP}{ND}=\frac{h}{x} \thinspace\thinspace and\thinspace\thinspace \frac{KP}{KA}=\frac{h}{x}\\\\\frac{PD}{ND}=\frac{h}{x}-1 \thinspace\thinspace and\thinspace\thinspace \frac{AP}{KA}=\frac{h}{x}-1\\](https://tex.z-dn.net/?f=%5Cfrac%7BND%7D%7BNP%7D%3D%5Cfrac%7BCD%7D%7BMP%7D%20%5Cthinspace%5Cthinspace%20and%5Cthinspace%5Cthinspace%20%5Cfrac%7BKA%7D%7BKP%7D%3D%5Cfrac%7BAB%7D%7BPM%7D%20%5C%5C%5C%5C%5Cfrac%7BND%7D%7BNP%7D%3D%5Cfrac%7Bx%7D%7Bh%7D%20%5Cthinspace%5Cthinspace%20and%5Cthinspace%5Cthinspace%20%5Cfrac%7BKA%7D%7BKP%7D%3D%5Cfrac%7Bx%7D%7Bh%7D%5C%5C%5C%5C%5Cfrac%7BNP%7D%7BND%7D%3D%5Cfrac%7Bh%7D%7Bx%7D%20%5Cthinspace%5Cthinspace%20and%5Cthinspace%5Cthinspace%20%5Cfrac%7BKP%7D%7BKA%7D%3D%5Cfrac%7Bh%7D%7Bx%7D%5C%5C%5C%5C%5Cfrac%7BPD%7D%7BND%7D%3D%5Cfrac%7Bh%7D%7Bx%7D-1%20%5Cthinspace%5Cthinspace%20and%5Cthinspace%5Cthinspace%20%5Cfrac%7BAP%7D%7BKA%7D%3D%5Cfrac%7Bh%7D%7Bx%7D-1%5C%5C)
![KA(\frac{h}{x}-1)=AP](https://tex.z-dn.net/?f=KA%28%5Cfrac%7Bh%7D%7Bx%7D-1%29%3DAP)
![ND(\frac{h}{x}-1)=PD](https://tex.z-dn.net/?f=ND%28%5Cfrac%7Bh%7D%7Bx%7D-1%29%3DPD)
Adding above two, we get
![(KA+ND)(\frac{h}{x}-1)=(AP+PD)](https://tex.z-dn.net/?f=%28KA%2BND%29%28%5Cfrac%7Bh%7D%7Bx%7D-1%29%3D%28AP%2BPD%29)
⇒ ![(KN-AD)=\frac{x}{(\frac{h}{x}-1)}](https://tex.z-dn.net/?f=%28KN-AD%29%3D%5Cfrac%7Bx%7D%7B%28%5Cfrac%7Bh%7D%7Bx%7D-1%29%7D)
⇒ ![a-x=\frac{x}{(\frac{h}{x}-1)}](https://tex.z-dn.net/?f=a-x%3D%5Cfrac%7Bx%7D%7B%28%5Cfrac%7Bh%7D%7Bx%7D-1%29%7D)
⇒ ![a-x=\frac{x^2}{h-x}](https://tex.z-dn.net/?f=a-x%3D%5Cfrac%7Bx%5E2%7D%7Bh-x%7D)
⇒ ![x^2=ah-ax-xh+x^2](https://tex.z-dn.net/?f=x%5E2%3Dah-ax-xh%2Bx%5E2)
⇒ ![x(h+a)=ah](https://tex.z-dn.net/?f=x%28h%2Ba%29%3Dah)
⇒ ![x=\frac{ah}{a+h}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7Bah%7D%7Ba%2Bh%7D)
Answer:
<h2>16/18</h2>
Step-by-step explanation:
<h2>hopes this helps. Mark as brainlest plz!</h2>
Answer:
what im confused any body else ?
Step-by-step explanation:
Answer:
gurl download Symbolab right now!!